"If anyone comes after me and does not hate... "Hate" is not primarily a feeling word in the Aramaic language, the language Jesus spoke. It is primarily a priority word. It means to abandon, to leave aside, to reject, or to love less than the other (comparative). A good example is that Jacob was loved and Esau was rejected, or "hated." Another good example is the story of Jacob: "and he went in also unto Rachel, and he loved also Rachel more than Leah, and served with him yet seven other years. And when the LORD saw that Leah was hated, he opened her womb: but Rachel was barren" (Gen 29:31). Jacob's desire for Rachel rather than Leah is the point.

So in this case Jesus is probably expressing the need for kingdom commitment to abandon all other allegiances. Jesus is not suggesting feelings of hatred toward people who we would otherwise love and care about. The opposite is actually being stressed here. The disciples separating themselves for mission in the kingdom underscores their devotion to Jesus because they have left the ones they loved.