Matthew 10:34-36

Look at Matthew 26 (specifically 52) where Jesus stopped Peter from defending him with his sword. Jesus is opposed to violence, full stop.

The sword Jesus spoke of in Matthew 10 wasn’t a literal sword. He’s saying he’s here to disrupt the status quo. Following him requires being at odds with the status quo (Jewish law), which is likely to result in being excluded from families and whatnot. He certainly doesn’t condone violence, but he does acknowledge that this is a fork in the road and people need to pick sides, because they can’t do both.

This similar idea is conveyed in Matthew 6:24 (replace “money” with anything else that stands between you and following God):

No one can serve two masters. Either you will hate the one and love the other, or you will be devoted to the one and despise the other. You cannot serve both God and money.

Or Matthew 5:29:

If your right eye causes you to stumble, gouge it out and throw it away. It is better for you to lose one part of your body than for your whole body to be thrown into hell.

I also don’t think he means you need to preemptively abandon your family, just that if you have to choose, choose God.

The same idea is true in secular ideology as well. If your family are Nazis, it’s better to leave them than become a Nazi.