Well, you don't! But what you can do is take away the power struggle surrounding it. You make it clear to him that you understand if he's getting to old for naps. Nonetheless, everyone needs a little time to themselves every day to recharge. You'd like to use 30 min (whatever) to get some exercise. Tell him that he doesn't have to take a nap, but he does need to play quietly in his room, and give you that time to yourself. I limited my boys to things they could do on their bed-looking at books or coloring, puzzles etc. Things that are quiet. Make sure he knows that it's ok if he does want to go to sleep, but he doesn't have to. Let him know you will be right there if he needs anything really important, but that you believe he is old enough to spend some time playing by himself.
This is the way I have done it with all of my kids, usually starting around age 2.5. Once I took away the struggle, I found that often times they fell asleep. My boys are 8 and 6 now, and we still have daily "quiet time". (Calling it that instead of naptime helped too)My boys know now, because we've always done it, that between 2-4pm, they are going to be in quiet time.
Three yr olds are able to be rational, and this is a good way for him to learn to play independatly, to listen to what his body needs, and to respect other peoples needs ahead of his own. Good practice for life, eh? You may need to really be vigilant with him. He is probably going to test you by coming out, but just calmly say, it's quiet time now, I'll play/get snack/read book etc when QT is over. Setting a timer might help too
Good luck! You deserve this time for yourself. It will make you a better mommy in the end. Mentally rested, physically healthier and energized.