Answer for : 對...負責;因為...被罰 | 代表sb講嘢

e.g.1 As a government, they should answer for their failure to sort out the problem.

e.g.2 I can answer for my parents as I know their position on this issue.

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Argue out : 爭論一個問題(problem)去找一個解決方案/法

e.g. If we can't argue our differences out, we'll have to take them to court.

但是

Argue sb into/out of doing sth : 說服sb不做sth

e.g. They argued him into withdrawing his complaint.

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感覺上手了~