The mother is asking Mikoto to give advice to Kazuki. Mikoto asks "Why do I have to do it?" (= "Why don't you do it yourself?"). The reason is that Kazuki simply refuses to talk to his mother (about the problem he's presumably having). He might confide to his sister however, and she in turn (as his sister) would be in a better position to understand and help him - at least, that's what the mother thinks.