Especially in high school, I was uncomfortable being naked in the changing rooms. I was aiming for a masculine persona and my body was neither as masculine as the other boys nor as feminine as a girl's. Not all of the boys believed that I had well-developed pectoral muscles. Anyway, trans people are by definition uncomfortable with their bodies.
The thing about girls hiding their breasts is entirely cultural, though. Until I was about 10, girls my age thought nothing of swimming topless. I have also visited a number of communities in different parts of Africa where even adult women often went topless - some of the rural Zulus in South Africa, Himbas and Tjimbas in what is now Namibia, San in Botswana and some of the more remote Samburu in Kenya, as well as Hamar, Mursi, Karo, Konso and Dassanech in Ethiopia. I am old now, so things may have changed since then.