I think society is against suicide mostly because it makes people sad when someone they know commits suicide. They would prefer it didn't happen. It makes them feel guilty, like maybe they could have done something to prevent it. Of course, I don't think basing one's decisions off of other people's feelings is in general considered to be a good thing. I think it's considered to be poor boundaries. But people don't usually apply that to the decision to commit suicide, for some reason.
Also, people assume that if you want to kill yourself then you must necessarily have something mentally wrong with you and not be thinking clearly. Therefore, in their view, you need treatment, not death. I suppose I can kinda see where they're coming from on that one. In some cases that is indeed the case. Probably is the case for me whenever I'm suicidal. But just because treatment exists doesn't mean the person can afford it or that it's otherwise accessible to them. So what are they supposed to do then, just keep suffering?
Also of course as others have mentioned there is the Christian thing.
EDIT: Also, I think in capitalist societies we have this idea that anyone could be anything. That there are no limits to what one could become. The poorest person can theoretically become a billionaire, and vice versa. So in other words, why are you killing yourself when it could get better, why are you killing yourself instead of going back to the grind and climbing the ladder? Of course, the issue is that the chances of a person from a poor background becoming a billionaire are extremely, extremely slim. So close to zero as to not really be worth considering. Yet that is what people uphold as proof that our current economic system is wonderful and the best possible one.