Chicken costume coukd be a way to say that he is mother hen.
Maybe they're worried about how their son and the people around him would react to two men looking after him.
I think so too, it's not very common where you can see 2 guys raising a dad. Maybe they scared other kids will bully him and neighbor gossips. U know people still not that comfortable with gay, especially one with kid, so sad but truth. ╮(￣▽￣)╭
He has severe childhood trauma, is painfully shy and introverted. He hides inside the costume to protect him from the world. It's a safe place when he's never really had one, and Dad knows that this is his form of self protection. Also, I think he hides because of the whole gay male mom stigma.
I wonder whats the reason behind the bird costume. I can sense a deeper storyline here soon