Why do some men have a mole with hairs exploding out of it?

They don't care: Most men are hairier than most women. The presence of hair coming from a mole reflects this. And most women would probably have such a mole (nevus) removed, while many men wouldn't care or would like it. A person has a choice -- one person will like a lesion that another person detests. Either gender can have a hairy mole or a larger hairy pigmented lesion.