Smart People Rationalizing
In the second panel, the character in question says "how can I trust myself to know the truth about anything?" This shifts the point from being "a pox on both your houses" to an expression of legitimate self-doubt. Anyone who engages in political debate for any significant length of time will discover how resistant people's opinions are to being changed by the force of the better argument. This intransigence naturally suggests that there are a lot of "smart people rationalizing," and it's reasonable to self-reflectively ask whether you are one of them.
Mandolin implies that this feeling that all sides may be rationalizing only happens for people in a position of privilege with respect to the issue being debated, because those who are suffering oppression have direct experience of its wrongness and a personal stake in getting the right answer. I would question this on two grounds -- first, because even if your experience of oppression points you in the right direction, it's highly doubtful that it provides all the details of the proper analysis and solution. That is, a woman's experience may tell her that feminists are substantively right, but it doesn't conclusively settle the debate between liberal, socialist, radical, eco-, and other forms of feminism. Second, it takes some reflection -- including confronting the possibility that you may be rationalizing -- to be sure that your experience is pointing you in the right direction. Many men's rights activists and others in objectively dominant groups genuinely feel oppressed. It takes a process of self-examination to determine whether one's felt oppression is real or the product of narrow vision and an illegitimate sense of entitlement.
Further, there's good psychological evidence that most political arguments are in fact "smart people rationalizing." Psychologists have shown that most of our moral commitments are made through an unarticulated, "intuitive" process. Articulated verbal discourse about our views comes after, reconstructing (from a quasi-outsider's position) the reasons for holding our view rather than revealing or expressing (from an insider's position) the actual causes of the belief. This does not mean that our positions are random, unreliable, or wrong. It simply means that our political discourse does not entirely match our intuitive thought processes. So it's difficult to use the conscious tools of political discourse to verify the reliability and accuracy of our own intuitive thought processes, or to change others' minds. And therefore periods of doubt of the type expressed by the cartoon character are legitimate and even necessary.
*Original version of this post misattributed the post I'm responding to to Maia.