What's private is what's inside me, what I may or may not choose to make known to you. My body is my body and it's just another work of nature with no surprises -- except for the variations which come along.
Towels are for drying oneself or for sitting on. They are not a garment to be worn! Whether you see my face, my crotch or my butt, it's all the same to me -- and they're not that different from other guys' areas.
Sorry, I think that keeping yourself wrapped up is hard to understand -- and what you've said still doesn't explain it to me.