The answer to this question can be found in Act I scene 2, when Orlando reveals his identity to Duke Frederick after winning the wrestling match against Charles. Note how Duke Frederick responds to finding out that Orlando is the son of Sir Rowland de Boys, who is an ally of the banished Duke Senior:
I would thou hadst been son to some man else.
The world esteemed thy father honourable,
But I did find him still mine enemy.
Thou shouldst have better pleased me with this deed
Hadst thou descended from another house.
Thus Duke Frederick dislikes Orlando because of the way that he is related to one of his enemies. This automatically taints Orlando by association, making Duke Frederick misinterpret Orlando and his actions and speech. Ironically, it is Orlando's victory that brings him to the attention of Duke Frederick and leads to his fall in favour in court, necessitating his removal to the Forest of Arden.