I understand what you're getting at with the fallacy (lets call it 'winning by not fighting'), but I don't think it applies here. There is too much difference between ending your life and choosing not to create another. Also related is the difference between not having children (logical end: no more humans) and having one child fewer than you would under better circumstances (logical end: decrease in population until circumstances improve).

That said, I'm biased because I don't want any kids right now. If I had one, suicide would probably follow anyway.