carrust. You have to have enough faith in yourself as a father to know what kind of man you have raised. Is your son really the sort of man to have love/hate on his knuckles, swastikas on his arms, etc?
The best you can do is sit down with your son and explain your concerns, why you don't like tattoos and what problems you think may arise with him having one.
You haven't mentioned what design he wants, it's size or where he wants it. It may be a relatively small tattoo he wants, in a place that isn't on show all the time, eg his back, shoulder, top of arm, etc. Again talk it through with him...it may not be easy for you...but it will show him that you accept him for the man he is.
At the end of the day you must accept he's and adult and it's his body, he is not affecting anyone else but himself. He may regret it later - he may not - but it's his decision and he will have to live with it.
I'd hate to think you're saying that you'll throw him out of the house because your son is daring to go against your wishes! It's the tattoos you hate not him.
He has a long future ahead of him...it would be such a shame for both of you to damage your relationship - possibly permanently - over this.