I never got the whole thing where people only identify a series with one console or the other. I've played Metal Gear on NES, PSX, PS2, Xbox, Xbox 360, PS3, PSP, PS Vita, GameCube... Hell, I have the Bleemcast disc somewhere around here for it as well.
It's pretty easy to understand. Despite Metal Gear, as a series, starting in the 8 bit era, it wasn't until MGS hit the Playstation 1 that the series became a huge phenomenon.
MGS1? Playstation 1 debut
MGS2? Playstation 2 debut
MGS3? Playstation 2 debut
MGS4? Playstation 3 debut (and exclusive)
MGS5? Multiplatform debut
And the PSP even got 4 MG(S) games, 3 exclusive to the platform, with Peace Walker debuting on that Platform. Hell, you can pretty much play all the games on PS hardware. That's why it's identified as a PS franchise, just like FF or KH, and others.