I wouldn't say I'm anti space exploration, but I don't really think its a great idea. Economics and sciences are both pretty good reasons to do it, but it will be a while before economics becomes viable, and scientific progress isn't exactly explosive even in the private sectors of space exploration development where they have money.
The drive to explore is nice, so long as I'm not the one who has to pay for it, especially since it is going to be a one way trip for the vast majority of explorers. I certainly don't fault people for saying 'I want to go out and explore in space', I just don't want to do it myself and I can't reasonably say that other people should.
Staving off the extinction of the human race is an interesting one to me, because I guess my disinterest in this argument shows my own weak connection to my species? I'm not trying to be edgy here, I honestly don't feel attached enough to my fellow man to care if after I'm dead the species goes extinct.
I do wonder why it is so important to some though, primarily because if some humans actually did manage to survive the trip and landed to make a new home... Generations living and adapting in space, in a completely different part of the galaxy, with no way to communicate with Earth, are those really still humans? Even if so, do you really feel some sort of connection with them, despite the fact that you could never really be sure that they still exist?