A surprising amount of what we do is down to how we think others will perceive us. I know plenty of adults (including myself) who would skip a shower and not shave or slob around on days when I know I'm not going out and won't be seeing anyone. I'd feel aggrieved at being punished for this too.
I know it's not quite the same thing but your son is getting to the age where he should be taking more responsibility for himself. It might be useful for him to be told by his peers (as opposed to his parents). When I hit adolescence, it took me a little while to adjust to wearing deodorant every day. My friends soon told me about it when I didn't and I started wearing it just to fit in and be like everyone else. I don't give it a second thought now, of course, but I did need a nudge from my peers.