Don't see it happening. PS2 had a lot of advantages. As it was declining in the major markets, a lot of new markets were opening it. It also was so dominant during its gen that developers kept supporting it for quite a while after its launch. Also, Sony wanted to keep pushing the PS2 after the PS3 was released, perhaps due to overconfidence. Nowadays, it seems like companies are much more interested in getting people to buy their newer products, which is why we didn't see a major drop in price or significant bundles for the PS4 when the PS5 launched.

Unless the Switch has very significant revisions that are all counted together for sales purposes (such as Gameboy/Gameboy Color) I don't see the Switch hitting PS2 numbers. But, the fact that it doesn't seem totally insane is pretty good for the Switch.

Are you sure about that?  The best selling Monster Hunter on PSP that I see is Monster Hunter Freedom 3 with 4.9m sales.  Total shipments of World across PS4, XBox One, and PC are 16.8m.  Pretty sure 1 of those platforms would have to gone over 4.9m by itself.

The Switch literally has all of the advantages you mentioned.

"As it was declining in the major markets, a lot of new markets were opening it."
The Switch is doing a lot better in RoW than any previous Nintendo console.  It is reaching new markets.

"It also was so dominant during its gen that developers kept supporting it for quite a while after its launch."
Third party support keeps increasing for the Switch.  Third party support for Switch in 2021 will be far better than every year before it, and 2022 will likely be better than that.  That is because 1) handheld developers are taking a long time and 2) home developers took a couple of years to take the Switch seriously.  On the handheld side we are just now getting successors to several 3DS titles (Monster Hunter, Bravely Default, Rune Factory, ect...), because Switch is a lot more powerful than 3DS.  These handheld developers are adjusting to the big bump in power.  Home console developers didn't want to back another Wii U, but it's very obvious at this point that Switch is going to have a huge install base.  New games usually take about 3-4 years to develop.  Up until now Switch mostly got ports, but we are actually getting to the point where Switch is getting its first wave of original 3rd party games.  Expect later waves to be even bigger than the first wave, because that is how it is on every successful console.

"Also, Sony wanted to keep pushing the PS2 after the PS3 was released"
Nintendo supported the 3DS for two years after the Switch released.  If they will do that for a system that sold about 76m, then how much longer will they support a system that will sell about twice that amount (or more)?

On top of that Switch has even more advantages over the PS2:
-Switch is currently tracking ahead of the PS2.
-Switch has still not had a price cut.  PS2 had several price cuts by this point.
-Switch is selling to both home and handheld markets.
-Nintendo are pros at selling multiple handheld systems to the same household.
-Switch has several evergreens that have already outsold the top selling PS2 game and will likely get more.

https://www.vgchartz.com/games/games.php?page=1&name=monster%20hunter&order=TotalSales&ownership=Both&showtotalsales=1&shownasales=1&showpalsales=1&showjapansales=1&showothersales=1&showpublisher=1&showdeveloper=0&showreleasedate=1&showlastupdate=1&showvgchartzscore=0&showcriticscore=0&showuserscore=0&showshipped=0

It's complicated to count considering Capcom kept making rereleases and revisions of their games, but if we look at it by platform, the handheld games seem to do better. The difference with World being the game could sell on three platforms at once, whereas the PSP and 3DS ones were exclusive.

These numbers for MHW are not just outdated, they are way way to low even for the time of the last update. On PS4 the game should be around 8M units iirc, 2M on XOne.

Lol to all the “no” and lmao to all the “no chance”

I am now certain the Switch will beat by more than 10 millions the PS2, but the console has started to definitely decline this month.

Pretty much this indeed

The PS2 was in a different situation where new markets were opening up quickly as the PS2 was winding down in the west, and the next gen consoles were prohibitively expensive. With the Switch those markets already are part of its current success, so they're not going to cause a late surge. There's also an issue of piracy in those markets which made certain systems really attractive like the PSP. Not sure how the Switch stacks up in terms of anti-piracy, but if Nintendo has successful measures, that would decrease the success it will have there. 

Whatever you want to say about the Switch's third party support, it was nowhere near the level of the PS2.

Not sure how much Nintendo supported the 3DS. For the end of its life it got mostly ports like Epic Yarn, Wario Ware, Mario Party, etc. The last "major" game it got was Samus returns. Even in 2016 support was pretty light in terms of major releases. Aside from Ultra Sun/Moon (Pokemon Company does its own thing) Nintendo wasn't giving major support.

Comparatively Sony was releasing major games pretty late into the PS2's life. Gran Turismo 5 and God of War was 2005, Soul Calibur 3 was I think 2006, There was a Socom in 2006, and they released other more minor stuff like Eye Toy Buzz. Even as late as 2009 they were porting PSP titles over like Ratchet and Clank and Jak and Daxter. They were a bit more aggressive with price cuts and such as well.

And, Nintendo has a history of not supporting their systems very well as a new one is coming out. They didn't do much for the Wii after Skyward Sword. Aside from Pokemon, they cut support from the 3DS pretty quickly as well, despite it being a massive success. Unless they change course, I wouldn't expect to see the Switch being pushed hard.

Switch is tracking ahead, but I'm pretty sure that the same could have been said for the PS4. The PS2 sold about 1/3 of its units after the PS3 came out, and that kind of thing hasn't been seen since. The Switch would probably need about 120-130 million or so before a successor is released to have a chance. It's possible, but iffy.

As long as Nintendo doesn't release the Switch's successor prematurely, then yes, it will.

The system is on course to pass the Wii by the end of the year before even factoring in a new model releasing and will still be shipping close to 20m units in 2023.

Switch will outsell Playstation 2 by the time it's 8 years old (March 3, 2025).