Q - Does Luke 14:26 Teach us to hate Others?

A - No of course it doen't, God is love and he tell us to love others.

Luke 14:26
If any man come to me, and hate not his father, and mother, and wife, and children, and brethren, and sisters, yea, and his own life also, he cannot be my disciple.

We must soften the face meaning of the word 'hate' to something like 'love less' and this is perfectly in line with the context of the ancient world, and the Jewish culture in particular.

Luke 14:26 falls into a category of "extreme language," the language of absoluteness used to express a preference, and may refer to disattachment, indifference, or nonattachment without any feelings of revulsion involved. To seal this matter completely, let's look at some parallel materials which prove our point. The closest example comes from:

Genesis 29:30.
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.

Here, "hated" is clearly used synonymously with one who is loved less. Let it be added that if Jacob hated Leah in a literal way, it is hardly believable that he would consent to take her as his wife at all! (See also Judges 14:16 and Deut. 21:15-17.)

Now here is another example from Jesus:

Luke 16:13:
No servant can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other.

Such extremes of feeling would be atypical, but the extremes are not meant to be taken literally; the point is that one master will get more dedicated labor than the other. Now let's move into some secular works with the same sort of hyperbolic language. Fitzmeyer's Lukan commentary offers this example from Poimandes 4:6:

If you do not hate your body first, O child, you will not be able to love yourself.

Would critics suppose that this teaches literal hatred of the physical body? It does not -- it emphasizes the need to give preference to the whole self before the body alone. Literal hate of the body would have us cutting it with razors or hitting it with blunt objects -- an extreme practiced in some Eastern faiths, but not among the Greeks!

Here is another example from a war song in the Poetae Lyrici Graeci (see James Denney, "The Word 'Hate' in Lk. 14:26," Expository Times 21, 41-42): it is said that in battle, men "must count his own life his enemy for the honor of Sparta" -- is this a literal hatred of one's own life being taught? No! It is emphasizing the need to make one's life secondary for Sparta's sake. Here's a final example from Epictetus 3.3.5: "The good is preferable to every intimate relation." This is just a more abstract version of Luke 14:26!