Um.....OF COURSE IT MADE NO SENSE! That was the whole point. I would imagine that the OP isn't married and has kids. Speaking as someone who is, as misplaced as dead wrong his actions were, I could identify with his feelings. If my family was lost in a cataclysmic event, I'd probably go apeshit and go after whoever was responsible. It might be wrong, but in that state of mind, I might not care. If I lost everything that mattered to me, I'd go all out because I'd have nothing to lose, which is why Nero was prepared to die.
It's time for Trekkies to get out of that logical post TNG mindset and realize that this new Trek is dealing with real people with real emotions.
I can understand what you're trying to say here; if your family were, say, killed in a school shooting or a terrorist attack, certainly, it'd be reasonable to expect you to want to hunt down those responsible, and depending on temperment, even to take revenge on them yourself.
But we're talking about something more than that. Carrying through with your example and lining it up with the film, after losing your family to a cataclysmic event you would wait for twenty-five years without either committing suicide or working through your grief, track down someone who tried, but failed, to help your family, kidnap them, make them watch as you killed, say, their entire home town, then leave them alive in the middle of nowhere and drive off to go kill the population of the nation's capitol. Now, how reasonable does that sound, maddened by grief or no?