Picture the sentence in a real family setting: a mother says her children look or behave like their father. The only word among the four choices that fits a family context is one about similarity.
"Idolize" would need feelings of admiration mentioned somewhere, which the sentence does not have. "Disagree" and "misunderstand" both describe a conflict or confusion between people, and the sentence describes the opposite, a natural similarity.
"Resemble" is the only option that captures children sharing looks or traits with a parent, so it lines up with the everyday use of "take after" in English.
The idiom "take after" therefore means option B, "Resemble".