I think the reason they are the 'big three' is that they were the three biggest Nintendo made hits starting on the NES and continuing on. Think about it:
NES
-------
Super Mario Bros 3
The Legend of Zelda
Metroid
SNES
-------
Super Mario World
The Legend of Zelda: ALTTP
Super Metroid
Many people consider Super Metroid the best game on the SNES if not of all time.
N64
-----
Mario 64
The Legend of Zelda: OOT
Metroid missing at the N64 point, but by then the legacy of the big three Nintendo franchises have been formed. They are the three Nintendo franchises that many see as defining Nintendo and have a much longer history than any other big ongoing franchise. There is a reason it seems most people pick Mario, Link or Samus when playing SSB.