I think it was a few things.
First off Sony had completely taken over the popular consciousness of video games. Playstation was the thing to have and PS2 just dominated.
You also have Microsoft entering the field to further increase competition. While Xbox barely did better than Gamecube, it could boast the best graphics whereas without it GC would clearly have been the graphically superior system. Plus Halo and Halo 2 were huge games and helped make Xbox compete as the multiplayer system of choice with GC after N64 had been the dominant multiplayer system of choice.
Also it looked like a toy. I think certain people just didn't take it seriously because of the way it looked.
It also had weird button configuration on the controller that people just found too weird to play.
They also once again choice an inferior software format.
Plus third party support, while far better than N64, was still hurting from the exodus that happened on N64.
Also Mario Sunshine was received that well because it was different and Wind Waker wasn't received that well because it was different. So Nintendo's two most iconic franchises were, at the time, considered kinda off versions when they came out.
So while Microsoft came in and said hey look we've got online games and we're the most powerful system and we've got Halo, and Sony was continuing the juggernaut brand that started on PS1 and got the lion's share of third party games and GTA got insanely popular, Nintendo basically was like oh hey we have a small inexpensive system that looks like a toy with weird buttons, no online, we're finally using discs but they are smaller and more expensive, and we've got less third party games.
Gamecube was a great system with a great library, it was cheap and powerful, but I think it kinda lacked a marketing hook.
