NATO is not
obligated to fight for Ukraine. That is true.
The question is, does NATO need to fight on its own behalf? I would say no, for two reasons.
First, even if Russia rolls over Ukraine, will that leave NATO enough worse off that it justifies going to war? No, I don't think it will.
Second, "you pushed me into it" is Putin's logic (or at least his very flimsy excuse) for invading Ukraine. I really don't want to use the same reasoning.
The only reason that I might buy is that it is morally necessary - necessary because we believe in freedom, and Russia is trying to take away Ukraine's freedom to choose their own future. I'm most sympathetic to that argument, but we've usually only used that in cases of genocide, and sometimes not even then. Ukraine clearly is not at that point... yet.