Several reasons.

- Mario Sunshine, Zelda: Wind Waker, Mario Kart: Double Dash, and Metroid Prime while good games did not live up to Mario 64, Zelda: OoT, GoldenEye, and Mario Kart 64. Even though I get with time these GCN games have established legacies now, at the time cell-shading Zelda was extremely unpopular, an entirely tropical Mario game with no ice/snow and other traditional style Mario levels was not a popular choice, MK:DD lacked tracks and a popular battle mode. Metroid Prime while brilliant was a slow paced single player game, not the huge crowd please that the multiplayer GoldenEye was.

- The purple design of the console while novel and again more easily appreciated with time was the worst design they could have chosen. Early 2000s pop culture was very much into "harder/cooler design asthetics". Hip hop, the Matrix movies, etc. were all the rage. The GameCube looked like an 8 year old's lunch box. Even kids didn't want it. They went way to kiddish in the look of the console.

- The $99-$199 price point which should have been an advantage backfired because when factoring in DVD playback, the PS2 and XBox were easily worth the extra premium in price, worse Sony cut the PS2 price so the GameCube's pricing was never that great.

- The headstart the PS2 got killed the GCN, they were already at like 18-20 million headstart before Nintendo sold even one system. In hindsight Nintendo should have moved to end the N64 cycle earlier and gone all-in for the fall 2000 GameCube launch (the hardware was finished). By fall 2001 it was game over.

- Resident Evil 4 was a spectacular system defining game, but by early 2005 that was too late, Nintendo needed that game for holiday 2002.

- Halo gave MS a stronger launch than what was expected and suddenly Nintendo found themselves in a dog fight for the no.2 spot, forget no.1 spot.

Not really sure why it failed. I liked the Gamecube a bunch and it was pretty cheap too. I guess the existence and popularity of the PS2 is the cause,

Personally I picked up a PS2 because I had a PS1, my friend had a PS2, and I liked the games that he played on his PS2, and I wanted to play them too.
I also picked up a Gamecube a few years later for the exact same reason. So pretty much I just followed my buddy.

Oh and I didn't even know the PS2 had a DVD drive until a year after I picked up a VHS IN 2005, which was also the same year I picked up a Gamecube.

There really isn't room on the market for three traditional consoles to succeed, there never has been.

In order to carve out its share Gamecube would've needed to convince consumers it was a better choice than PS2 and Xbox, and when those systems were delivering on megaton exclusives like Halo, Metal Gear, and Final Fantasy, plus better third party support, DVD support, better marketing, and looking like cool and serious pieces of hardware, there just wasn't any reason to buy a Gamecube unless you absolutely had to play Nintendo's games, and even those were at a relative low in terms of appeal at the time thanks to weird design choices.

In addition to the nostalgia that forms naturally over time, as Jumpin points out, the system has attracted a certain hipster-ish cult appeal in the years since in the way that a lot of failed systems do, when they're seen as cool precisely because they weren't popular.

As such, the internet tends to paint an unrealistically positive view of Gamecube as this amazing system that should have succeeded, when it reality it got pretty much everything wrong, from software to marketing to disc format to the controller to the way it looked. 

While I could agree that Mario Sunshine, Zelda Windwaker, MK Double Dash may have not lived up as a sequel to their N64 counterparts. Chill with calling Metroid Prime not living up to Mario 64 and Zelda OOT. Metroid Prime is too good of a game to disrespect like that and in terms of quality it's up their with Mario 64 and OOT. I know Metroid Prime wasn't really a system seller and a major seller for the GC, however in terms of quality it was great.

The first argument of why it failed that's mainly been agreed upon by many is that the games did not live up to Nintendo standards and didn't really take a step forward from the N64 era. While from a personal standpoint I disagree with this cause I personally loved the Gamecube's game library even Mario Sunshine & Windwaker. I see why the majority of people weren't interested in buying a GC since most of the games did not seem live up to the N64 quality of games, where games like Mario 64 and Zelda OOT set the gaming world on fire, the Gamecube didn't really seem to have any sort of game like that. Mario Sunshine, while I love the game, seemed a shameless sequel to one of the most revolutionary games of all time Mario 64 where the gameplay was so unconventional and in a lot of ways a step down from Mario 64 and didn't do anything to stand out like Mario 64 did, plus it didn't help that the marketing of the game was awful. With Windwaker, it was another less conventional Zelda game that used a cartoony-artstyle instead of the dark revolutionary Zelda game that everyone was hoping for, and it further pushed the idea that the Gamecube was a toy and a kiddy console. Many people who brought an N64 didn't seem interested in upgrading to a GC where the games seemed less impressive than their N64 counterparts.

Plus I think the lack of 2D games likely hurt the GC as well, since their seemed to be a bigger market of 2D games than 3D games. Comparing the sales of NSMB games to 3D Mario Games proved it, many casuals are turned off by a console that only has 3D platformers rather than simple 2D platformers. I believe that's one of the main reasons consoles like the NES,SNES,DS,Wii, did more successful cause of 2D Platformers, the GC had none.

It also seems like Nintendo didn't appeal to those who didn't purchase a Nintendo system before, some big violent games completed missed out of the GC giving the GC an image that you can't get hardcore experiences on it, plus it lacked RPGs, which is huge in Japan, ect..

Because Sony's marketing team absolutely killed it to the point that there are people who still believe the PS2 was the most powerful console of that generation. And the GCN did not play DVDs... and the general public are morons ;)

Wouldn't consider the GameCube a failure. The Wii U and PS Vita? Sure.

Plenty of factors, limited capacity of game storage, no dvd built in ( apart from the expensive panasonic q gamecube), as with N64 era, the development licence more expensive than microsoft xbox and sony ps2, no backward compatibility with previous gen n64 unlike ps2 with ps1, proprietary component video cable, limitations of different region gamecubes, example no RGB on ntsc consoles, but no s video on pal consoles, no online capabilities, over reliance of traditonal nintendo franchise while new franchises was not being emphasised, maybe they should off advertise Animal crossing more and appeal to new markets

gamecube sold around 21 million, xbox sold around 23 mil, ps vita is believed to sell around 17 mil which is that far off from wii u at 14mil and gamecube, therefore it's arguable any console not selling more than 30 mils is disappointing