Correct.

...and a man's enemies will be the members of his household. He who loves father or mother more than Me is not worthy of Me; and he who loves son or daughter more than Me is not worthy of Me. Matthew 10:36-37 (NAS)

As an example, many of the Jews who decided to follow Jesus were put out of the synagogue...and/or completely rejected by their own families. 

What would you think if your own relatives decided to persecute you for becoming a Christian?

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