Yu'er can write, but Wang Ye didn't let him.
And if you pay attention at the last pictures you can see he beated him up, he has purple marks on the body.
Okay, there can be misunderstandings, but that doesen't allow you to beat the shit out of someone.
He knows Yu'er can write because he teached him how to.
So why, if you love him so much and respect him, don't you let him explain himself?
That's why I said he isn't listening to Yu'er, he isn't giving him the chance to explain himself, in this case through writing. I don't think there were any bruises, it was the ink. This is from a different era where this was seen as "acceptable". I don't agree with him, I'm simply saying he isn't just being an asshole for no reason. It's natural to be upset, not in an abusive way, but he was raised believing it was okay. Look at his siblings, they get away with whatever.
Playing devil's advocate, but the way the prince is acting is solely based on misunderstandings, not solely because he's a horrible person. Don't get me wrong he is by no means perfect, but if you see the way he treated Yu'er before the Emperor then you can see he treated him relatively well and was protective of him (minus that one incident, I'm pretending never happened). He isn't "listening" to Yu'er. Yu'er can't talk, so he can't defend himself properly and explain his side of the story or the truth at that, so everything he knows is coming directly from the Emperor which leads to gross misunderstandings. Meanwhile Yu'er can only express himself with very limited facial expressions and physical gesture. I wish he would stop being so impulsive and let Yu'er write.