Bra age limit?

Do you think there's an age that's too young for a bra? My fiancés daughter came over today so excited to tell me about her bra. She's only five so I thought she was lying. But then she took off her shirt and revealed a training bra. She went on for hours telling me about all her bras and all the colors and patterns she has. I thought it was cute how excited and proud she was. But her father was upset. He was saying that she's way to young and doesn't need it. Then he claimed that her mother was trying to make her into a little woman and he wouldn't be suprised if his daughter was wearing make up and high heels next time he saw her. I do think she's really young for it but I don't think it's really causing any harm. I also feel like my fiancé is upset because he doesn't want his baby girl to grow up. Would you buy your little girl a bra if she asked for one. Like ages 3-6.