There are at least two major arguments against these types of discrimination.
First, there is a moral argument. According to this argument, people of all races and both sexes are born equal. Therefore, it is immoral to treat them as fundamentally different. Morality requires us to realize that we are all essentially entitled to the same opportunities.
Second, there is a pragmatic argument. This one holds that discrimination weakens an economy and society. Discrimination, for example, keeps us from fully utilizing the talents of women and non-whites. This prevents our society and economy from being as productive as it could be.