Why were segregated schools morally wrong?
The basic answer is that it denied equal opportunity to fellow humans.
The "morality" may be trickier, as it can be interpreted differently by different people. Generally, however, it is considered immoral to arbitrarily (or worse, due to bigotry) treat any human being any differently than any other human being.
You might also be interested in this self-test of Utilitarian Morality: