The text gives us absolutely no idea of why Oliver despises Orlando. We are told only that he does and has despised him. The offenses against Oliver as listed by Orlando are that
- Oliver has not educated him
- he has not trained Orlando in a gentleman's skills and deportment
- Oliver has fed and trained his horses better than Orlando
- he has educated in a gentlemanly fashion the second son and brother
- Orlando is cast off and not given a brother's accommodation ("the lodging where you use to lie")
We can only surmise from this scant information that perhaps Oliver resented Orlando's birth because he and the second brother, Jaques, were close, thus Oliver resented Orlando as an intruder. Perhaps, since Orlando is the youngest and since the boys' mother is never mentioned, Oliver resents Orlando because their mother died in childbirth. Perhaps Oliver resented Orlando because that meant sharing the wealth in one more direction; if Oliver and Jaques are close, then giving Orlando an allowance and his share of the inheritance would reduce Jaques' portion.
physic your rankness, and yet give no thousand
Shakespeare wanted us to know that there is deep ill will between the two brothers. He was not concerned that we know the "back story" of the ill will. Perhaps the Elizabethan audience, more versed in family issues of the day, could readily fill in the gaps of the story and arrive at sufficient understanding to make an explicit explanation unnecessary. Or perhaps Shakespeare simply thought a detailed explanation superfluous to the heart of the story.
My / father charged you in his will to give me good
education: you have trained me like a peasant,
obscuring and hiding from me all gentleman-like
qualities. The spirit of my father grows strong in
me, and I will no longer endure it: therefore allow
me such exercises as may become a gentleman, or
give me the poor allottery my father left me by
testament [i.e., will];
In addition, after Orlando wins the wrestling match against Charles, Oliver burns with envy against Orlando and seeks to have him murdered because of his feeling of envy.
Your brother [...]
Hath heard your praises, and this night he means
To burn the lodging where you use to lie
And you within it: if he fail of that,
He will have other means to cut you off.