Why does Duke Frederick dislike Orlando in As You Like It?

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.