What should you not do when evaluating an opponent's supporting points?

a.
consider whether the appeals are convincing
b.
look for arguments based on faulty assumptions
c.
question the opponent's family background
d.
ask if there's sufficient evidence

The answer is C: Question the opponent's family background.

This is a form of a logical fallacy called, ad hominem, which is Latin for “to the person”. It addresses a faulty form of argumentation that, instead of focusing on the topic that the person who is making the argument is presenting, the focus is instead on attacking the person that is making the argument by addressing his or her character, motive, background or other information that is not related to the substance of the argument.

What you should not do when evaluating an opponent's supporting points is C. Question the opponent's family background

Explanation: An opponent's supporting points are refuted in an argumentative essay. The writer of this essay must evaluate and criticize his/her opponent's ideas in a clever way. In other words, the writer needs to strengthen his/her piece of writing to sound more credible by weakening the arguments of the opponent. The writer of the argumentative essay should look for arguments based on faulty assumptions, ask if the opponent presents enough evidence and if his/her ideas are convincing. However, he/she should not question the opponent's family background because this is not connected at all to the arguments that will be refuted and this questioning could end up weakening his/her own essay rather than the opponent's supporting points.

a and b are the correct answer to what your looking fior