Panel 1: Mike continues to infuriate Elly by telling her to change her appearance. This time around, she's gotta endure static about that low-hanging ponytail she's worn for the last twenty years and how she should get it cut or something.
Panel 2: He doesn't notice that he's pissing her off by yapping about how old fashioned and out of style she looks.
Panel 3: Having had enough of being dictated to by the irritant, she lashes out and tells him to do something about his own hair before talking about other people's. Why, she can barely tell him from Farley, his hair is so messy.
Panel 4: Since Mike is lacking in awareness of any sort, he growls about how every time he turns around, he gets criticized.
Summary: The reason that he can dish it out but he cannot take it is that while being bullied is bad because his feelings hurt, his teasing others is harmless because other people do not have feelings that can be hurt.