Imagine that all the people who believed in climate change - globally - committed suicide in some appropriately low-carbon manner. Everyone remaining does not believe in climate change. How long does it take the population to bounce back, and what sort of global warming mitigation do you think happens? Does the world in this thought experiment end up emitting less carbon?
Individual actions might have next to no effect, but institutional actions will. Giving up your opportunity to influence those institutional actions (whether through your own efforts or those of your children) is not beneficial to the environment. Of course, this calculus is different for the average person. But if you're the sort of person who's contemplating suicide to help the environment, you're exactly the sort of person that the world needs to not commit suicide.