The whole concept of "generations" was made up by someone who made arbitrary decisions as to which console belongs to what generation.. It's never been clear. It's never been obvious. It's always been bullshit.
Don't believe me? Try to get this thread to come to a consensus of which generation the Gameboy belongs to. Try to explain how the Atari 2600 and the Atari 5200 are a part of the same generation. Explain how the Virtual Boy cleanly fits into all of this mess, and doesn't disrupt the "generation" of either Nintendo's home consoles or handhelds. You can't do it. You won't do it. Because there is no answer, and most importantly even if you had an answer, it doesn't matter at all.