Loads of places.

1. 599 US DOLLARS. Even ignoring that, taking the the $499 20 GB model into account, the PS3 was $100 more expensive than it shoul have been. Especially for a console with no HDMI cable and only 20 GB of storage. Even back then, 20 GB was not that great for a price of $500. Speaking of which...
2. Blue-ray. Making a console with a blue-ray player makes sense for the 8th generation consoles like the PS4, but for the PS3 in 2006? The PS3 only came out a few months after Blue-Ray officially did in 2006. In contrast, the PS2 came out about four years after the DVD was released. Having later PS3 models support Blu-ray might have been a good idea, but it was simply too expensive in 2006 to make the PS3 play Blue-ray discs. Especially since so few games would take advantage of them.
3. The Cell. It could be used to unlock huge power, but for most developers, it was simply easier to make a 360 game dumbed down for the PS3 than the other way around. True, 1st party games benefitted from the Cell, but unlike, say, Nintendo, Sony does not solely rely on 1st party games to sell systems. Even on the PS2, the only huge 1st party titles were Gran Turismo 3 and 4. Third Party devs that made games like GTA, Final Fantasy, Madden, Racing games, and some shooters were all more important than aany other 1st party franchises on even Sony's magnus opus console.
4. Online. The PS3 had pretty good online play, services, etc. However, until fairly recently, Xbox Live was a far better service, even if you had to pay for it. Considering how this was the generation of online play, this can be seen as the right strategy done a few years too late. Nintendo at least had the excuse of focusing on local multiplayer and being the "budget" console. The PS3 was too expensive to justify the less than stellar online services.
5. Continued PS2 support. Sony released a bunch of notable games for the PS2 for a while after the PS3 was out. Although this made some sense, it ultimately had its downsides. There were reasons the PS2 outsold the PS3 in 2007: two of them were games God of War 2 and Rogue Galaxy. Not to mention those lower budget games that could just have easily been used to improve the PS3 library early on. Incidentally.
6. Lack of Early Killer Apps. By the end of 1996, the time the N64 came out, the PS1 had killer apps like Crash Bandicoot, Tekken 1 and 2, Resident Evil, Rayman, and Tomb Raider. Each of those games sold over 3 million copies lifetime on the PS1 alone. By the end of 2001, when the Xbox and GameCube came out, the PS2 library contained gems like Gran Turismo 3, Grand Theft Auto 3, Final Fantasy X, and Metal Gear Solid 2. Each of those sold over 6 million copies on the PS2 alone! The PSP, by the end of its first year of life, had it's best-selling game: Liberty City Stories. The PS3, however, lacked extra time before the release of its main competitors. And even if we include all of 2007 as the launch period, the PS3 probably had it worse than the Wii U. Even though games like Resistance and Motorstorm eventually became hits, the PS3 only had one huge game until 2008: Modern Warfare, which played better on the 360 thanks to the above-mentioned online. Even 2008 wasn't that great; the PS3 had LBP and MGS4 as exclusives, but the 360 had Gears of War 2 and better online for other big games like CoD. Only starting in 2009/2010, when Microsoft lost momentum and Sony stopped supporting the PS2 and PSP, did PS3 exclusives become a big deal.
7. Motion Controls. The Wii was defined by its motion controls. Without them, the console probably would probably have only sold half as well. The Kinect, though not an indisposabole part of the 360 experience, breathed new life into the system in 2010 and 2011. The PS3 had the Move. It was not bundled with any great killer games, was not revolutionary, offered no new experiences, and generally did nothing noteworthy. Which would be acceptable, except that resources were wasted on advertising this thing and making both original games for the Move and adapting new games to incorporate it. Not to mention that some people were probably disappointed by the support it received.
8. Media. One of the big things that made the PS2 a huge hit was its ability to play DVD's at a low price. The PS3 promised the same thing, except with Blue-Ray. However, physical movies have largely fallen out of favor these past 5 or so years, with streaming services like Netflix becoming the new norm. And although the PS3 has Netflix, the 360 got it first and even the cheap little Wii eventually got it. Without this bonus advantage, the PS3 had another strike against it.
9. Handheld/Mobile Migration. Long story short, a lot of the big series of PS2 days have, over the past decade, shifted to handhelds. See Monster Hunter, Dragon Quest, and even some 1st party games like Jak & Daxter. Meanwhile, although mobile devices have hurt handhelds fart more, it's worth noting that a lot of major PS2 games were licensed titles. Spider-Man, The Simpsons, The Lord of the Rings, Harry Potter, and the like would today be released on mobile devices instead.  If you don't think this is valid, consider the following: Shrek 2 outsold Jak 3 on just the PS2. Think about it.
10. Strategy. Ultimately, unlike the PS1 and PS2, there was no plan to expand the video games audience using the PS3. It was simply assumed that the existing audience all buy the PS3 and would be enough. The Wii is the most notable alternative, but even the PSP offered something new, as it promised fans of other media a cool device while serving as a potential Trojan's Horse for bringing games in their lives.

Not true at all but we are good. No worries you can have it.

Loads of places.

1. 599 US DOLLARS. Even ignoring that, taking the the $499 20 GB model into account, the PS3 was $100 more expensive than it shoul have been. Especially for a console with no HDMI cable and only 20 GB of storage. Even back then, 20 GB was not that great for a price of $500. Speaking of which...
2. Blue-ray. Making a console with a blue-ray player makes sense for the 8th generation consoles like the PS4, but for the PS3 in 2006? The PS3 only came out a few months after Blue-Ray officially did in 2006. In contrast, the PS2 came out about four years after the DVD was released. Having later PS3 models support Blu-ray might have been a good idea, but it was simply too expensive in 2006 to make the PS3 play Blue-ray discs. Especially since so few games would take advantage of them.
3. The Cell. It could be used to unlock huge power, but for most developers, it was simply easier to make a 360 game dumbed down for the PS3 than the other way around. True, 1st party games benefitted from the Cell, but unlike, say, Nintendo, Sony does not solely rely on 1st party games to sell systems. Even on the PS2, the only huge 1st party titles were Gran Turismo 3 and 4. Third Party devs that made games like GTA, Final Fantasy, Madden, Racing games, and some shooters were all more important than aany other 1st party franchises on even Sony's magnus opus console.
4. Online. The PS3 had pretty good online play, services, etc. However, until fairly recently, Xbox Live was a far better service, even if you had to pay for it. Considering how this was the generation of online play, this can be seen as the right strategy done a few years too late. Nintendo at least had the excuse of focusing on local multiplayer and being the "budget" console. The PS3 was too expensive to justify the less than stellar online services.
5. Continued PS2 support. Sony released a bunch of notable games for the PS2 for a while after the PS3 was out. Although this made some sense, it ultimately had its downsides. There were reasons the PS2 outsold the PS3 in 2007: two of them were games God of War 2 and Rogue Galaxy. Not to mention those lower budget games that could just have easily been used to improve the PS3 library early on. Incidentally.
6. Lack of Early Killer Apps. By the end of 1996, the time the N64 came out, the PS1 had killer apps like Crash Bandicoot, Tekken 1 and 2, Resident Evil, Rayman, and Tomb Raider. Each of those games sold over 3 million copies lifetime on the PS1 alone. By the end of 2001, when the Xbox and GameCube came out, the PS2 library contained gems like Gran Turismo 3, Grand Theft Auto 3, Final Fantasy X, and Metal Gear Solid 2. Each of those sold over 6 million copies on the PS2 alone! The PSP, by the end of its first year of life, had it's best-selling game: Liberty City Stories. The PS3, however, lacked extra time before the release of its main competitors. And even if we include all of 2007 as the launch period, the PS3 probably had it worse than the Wii U. Even though games like Resistance and Motorstorm eventually became hits, the PS3 only had one huge game until 2008: Modern Warfare, which played better on the 360 thanks to the above-mentioned online. Even 2008 wasn't that great; the PS3 had LBP and MGS4 as exclusives, but the 360 had Gears of War 2 and better online for other big games like CoD. Only starting in 2009/2010, when Microsoft lost momentum and Sony stopped supporting the PS2 and PSP, did PS3 exclusives become a big deal.
7. Motion Controls. The Wii was defined by its motion controls. Without them, the console probably would probably have only sold half as well. The Kinect, though not an indisposabole part of the 360 experience, breathed new life into the system in 2010 and 2011. The PS3 had the Move. It was not bundled with any great killer games, was not revolutionary, offered no new experiences, and generally did nothing noteworthy. Which would be acceptable, except that resources were wasted on advertising this thing and making both original games for the Move and adapting new games to incorporate it. Not to mention that some people were probably disappointed by the support it received.
8. Media. One of the big things that made the PS2 a huge hit was its ability to play DVD's at a low price. The PS3 promised the same thing, except with Blue-Ray. However, physical movies have largely fallen out of favor these past 5 or so years, with streaming services like Netflix becoming the new norm. And although the PS3 has Netflix, the 360 got it first and even the cheap little Wii eventually got it. Without this bonus advantage, the PS3 had another strike against it.
9. Handheld/Mobile Migration. Long story short, a lot of the big series of PS2 days have, over the past decade, shifted to handhelds. See Monster Hunter, Dragon Quest, and even some 1st party games like Jak & Daxter. Meanwhile, although mobile devices have hurt handhelds fart more, it's worth noting that a lot of major PS2 games were licensed titles. Spider-Man, The Simpsons, The Lord of the Rings, Harry Potter, and the like would today be released on mobile devices instead.  If you don't think this is valid, consider the following: Shrek 2 outsold Jak 3 on just the PS2. Think about it.
10. Strategy. Ultimately, unlike the PS1 and PS2, there was no plan to expand the video games audience using the PS3. It was simply assumed that the existing audience all buy the PS3 and would be enough. The Wii is the most notable alternative, but even the PSP offered something new, as it promised fans of other media a cool device while serving as a potential Trojan's Horse for bringing games in their lives.