1) price, 99$ VS 299$.
2) Multiplatform.
3) Hardware in the second place.

Because the GC was a better console (for the time) at a cheaper price with better third party support.

You want Nintendo to sell the Wii U for $150?

Gamecube was cheaper plus it actually had some 3rd party support not miles better then the Wii U but still better.

Sony made all of their price cuts for the PS2 in the U.S. after the end of the fiscal year for reporting reasons.  All of the PS2 cuts in the U.S. were made a short time after the end of the FY in March.  

But the price cuts were like a game of tit for tat (or equivalent retaliation) that all 3 console makers were taking turns instigating.

Appropriate price, solid exclusive games, no confusing name, no hamfisted gamepad for the sake of differentiation. In the long run I see the Wii U doing just as well if not better though.

Surely it's the games selection.

The only thing that feels radically new is Nintendoland, but they decided to plaster old icons all over it and pump up the color until it became a confusing mess to look at.

It's a great game collection, but it's thoroughly unwelcoming to the public.

Everything else they got is sequels or stuff that FEELS old.

Nintendo made multiple mistakes with Wii U, like bad name, bad marketing, weak launch games, software drought, hardware not appealing for 3rd party....and GC really didn't have any biger problems except PS2.

Fisher price purple lunchbox design that automatically painted the system as a toy, not making the sequels to Mario 64/Zelda: OoT/GoldenEye that people wanted, losing the FPS auidence to MS, no DVD playback, etc. etc.

Nintendo made multiple mistakes with the GCN and got beat by both Sony and MS. 

Nintendo just can't help making mistakes, they make major ones each generation that gift the competetion a free pass to exploit them. 

Not to mention Gamecube atleast got some multi platform titles. And it matched it's competition power wise.