I think I'm not going to let my employee take 3 days off.
Why won't you give them the 3 days off?
I'm sure he's going to abuse the 3 days off by visiting his family for several days.
If your employee is due time off, you shouldn't worry about how they'll spend the time. You owe them time off as an employer, and you can't dictate how they use their time off.
I'm pretty sure that if I give him the leave, he will use it to visit his family. He asked me for 3-day off and I think that he would go to his family instead.
Does it really matter what he does on his days off? It's not like visiting family is a bad way to spend time off anyways. You should just let him do it, it's not a big deal.