That specific passage is about people coming to accept Jesus (and God), accepting truth, which naturally divides a fallen world where people have embraced lies. Look at the above passage when combined with Luke 12:49-53 and Luke 14:26:

“I have come to bring fire on the earth, and how I wish it were already kindled! 50 But I have a baptism to undergo, and what constraint I am under until it is completed! 51 Do you think I came to bring peace on earth? No, I tell you, but division. 52 From now on there will be five in one family divided against each other, three against two and two against three. 53 They will be divided, father against son and son against father, mother against daughter and daughter against mother, mother-in-law against daughter-in-law and daughter-in-law against mother-in-law.”

“If anyone comes to me and does not hate father and mother, wife and children, brothers and sisters—yes, even their own life—such a person cannot be my disciple.

These passages don't mean one should hate their family, or that Jesus is intentionally dividing families against themselves. It's that Jesus (and God) want us to prioritize him (truth) above all other priorities. It's identical to when a loved family member espouses a foolish thing, or does a foolish thing, and we correct them. Just because we love someone, doesn't mean we have to agree with everything they say and do. We must rebuke falsehoods and lies.