Are sports bras meant to be worn alone or under shirts?

 My dad constantly argues with me whenever I work out in a sports bra and shorts. He says that my BRA is too sexual, and that it needs to be covered. Personally, I get too hot too fast, so I can't just throw a shirt on and be fine! I also hate getting more things dirty than necessary, so I love working out in that outfit. What do you think? And I usually work out inside, but I like to go on a walk outside sometimes too. It's a small neighborhood and people mind their own business, so I don't see why my dad gets so angry whenever the topic of working out comes along.