Not every man needs to be a warrior. But every man should study martial arts at least long enough to reach a minimal level of standard. I would say about one year (typically around the green belt level in most Japanese systems) of adult level study at a serious dojo is a good minimum, although there is definitely no problem with more training.
Every man should have a minimum practical ability to protect himself.
Every man should have a minimum practical ability to protect his family, or he is not truly a man.
Your wife or girlfriend will find you hotter if you have some level of fighting skill – even if she denies it. This is usually even more effective with ultra-pacifist hippie chicks.
If, like me, you live in suburban America, you live in a generally safe world. However, that world is punctuated by intermittent, highly random bursts of violence. These bursts are entirely unpredictable. While there is plenty you can do to lower your exposure to them, there is nothing you can do to reduce that risk all the way to zero. You can, however, prepare for it and learn to deal with it. Follow the Boy Scout motto: be prepared.