It is more appropriate to reword the question as Duke Frederick's hatred towards his elder brother Duke Senior, because throughout the play it is Duke Frederick who acts with hatred towards his brother and we find no instance of Duke Senior retaliating in the same spirit. To begin with Duke Frederick usurps the position of Duke Senior and banishes him into exile. When many a lords express their solidarity towards the latter, the former wastes no time in confiscating their properties and send them on exile. Later on he also banishes the innocent and gentle Rosalind, the only daughter of Duke Senior by charging her of treason and even threatens to get her killed if she does not leave his court within the time limit of ten days. When Rosalind questions the reason for her banishment, Duke Frederick declares, 'Thou art thy father's daughter; there,s enough.' These instances clearly indicate Duke Frederick's hatred towards his brother Duke Senior.