Because that would remove Georgia from Russia's sphere of influence. They could no longer de facto dominate Georgia and Georgia would already be armed if a conflict with NATO started.
They do offer their own pact, called the CSTO, Collective Security Treaty Organization.
I think that's why they invaded Georgia, overt greed. To be fair that also plays a role in NATO expansion. NATO won't accept a country that can't pull its own weight unless it has some kind of strategic value or economic value. It must be worth defending.