I think we can relate the way in which Orlando, especially towards the beginning of the play, is constantly trying to prove himself by showing his physical dominance, can be related to the way he has been brought up by his elder brother, Oliver. The play opens with Orlando's speech where he clearly states his grievance against his older brother and the way that he failed to fulfil his father's wishes to bring up Orlando to be a gentleman:
His horses are bred better, for besides that they are fair with their feeding, they are taught their manage and to that end riders dearly hired; but I, his brother, gain nothing under him but growth, for the which his animals on his dunghills are as much bound to him as I... He lets me feed with his hinds, bars me the place of a brother and, as much as in him lies, mines my gentility with my education.
It is no wonder, therefore, that Orlando feels the need to endlessly prove himself by physically besting those around him. Having suffered such abuse in his upbringing and such slighting, he is obviously an individual that feels the need to prove himself at every step. This is in part what his experiences in the Forest of Arden cure him of.