^ Except that Q has never acted that way. Q has, from the beginning, acted as though humans carry a special interest for him, and that our heroes -- particularly Picard -- carry a special interest.
Yeah, for now. From our perspective, mayflies that we are, it seems like the attention he's showing us is lasting. But our definition of "lasting" is fundamentally different from his. Even if Picard got rejuvenated and lived to be a thousand years old, that would still be a tiny fraction of Q's multigigayear existence. It's likely that Q is going to continue to exist for billions of years after Picard dies. And it's safe to assume that Q has had many, many previous "pets" over the vast span of his existence. Picard and humanity are his current hobby, and he throws himself into it wholeheartedly, but if you place it in the context of his entire lifespan, the unavoidable conclusion is that it's just a temporary phase. It will end, and he'll move on.
It may not make sense when you think about the lifespan of the Q and what their attitude toward humans should be. But the on-screen evidence seems clear that Q is very interested in and concerned about humanity in general and Picard in particular.
Many of us have pets belonging to species that don't last very long. We care about them while they're with us, we do our best to keep them safe, but then they die and we get another one. I'm not saying he doesn't care at all; I'm saying there are limits to how important it really is to him. Losing your pet gerbil is sad, but it doesn't compare to losing your mother or your spouse of 40 years.