What does Never let your sense of morals get in the way of doing what's right mean?

There are so many divergent views of morality that some are bound to be wrong. Hence, many people may act out of a sense of morality, but they are not really doing what is right. But the quote by Asimov might be a bit more deep...people often rationalize their actions so that they twist their sense of morality to just do whatever they feel like doing, regardless of whether or not its right or wrong.