I disagree that suicide is illogical. There is nothing logical about a desire to continue existing. Logic simply has no bearing on such decisions.

This is why irrational drives are essential. Down there at the bottom of whatever logical structure you have built sits an irrational longing, desire or passion which keeps you going. For the OP it was a family and a drive for successful reproduction. It can be other things, too. Without a drive like this giving you a purpose, logic won't prevent you from self-destruction.