Beneatha mocks what she sees as Walter's submission to the white man and others. She sees him as less than a man because he still lives under Mama's roof and must submit in a sense to her. Walter can sense Beneatha's lack of respect for him as her older brother, and so the two have several confrontations stemming from their view of one another.
In contrast, Walter thinks that Beneatha needs to submit more. As her older brother, he thinks he has the right to order her about and to invest the money that Mama had entrusted him for Beneatha's schooling in his own dream. Walter is a dreamer, and because Beneatha is more a person of action, the two are bound to clash over their view of the future and how each of them should live.
In the end, although Beneatha seems to have gained respect for her brother after he passes up Mr. Lindner's offer, it is doubtful that two strong personalities such as she and Walter are could live completely at peace in the same house. Her hurtful words toward Walter earlier in the play would realistically not just fade away.