Another answer (which I’m not sure is the answer) is that in logic or mathematics, a person is more likely to be convinced by a random correct proof than a random flawed proof; and if a person is convinced by a flawed proof it is easy to change their mind by pointing out the flaw in the proof; but if a person is convinced by a correct proof, then it is difficult to change their mind by incorrectly claiming there is a flaw. Of course I am being sloppy and nontechnical here; I bet there is a subtle, technical sense in which, under reflection, Modus Ponens is more appealing than Appeal To Justin Bieber.
Another answer (which I’m not sure is the answer) is that in logic or mathematics, a person is more likely to be convinced by a random correct proof than a random flawed proof; and if a person is convinced by a flawed proof it is easy to change their mind by pointing out the flaw in the proof; but if a person is convinced by a correct proof, then it is difficult to change their mind by incorrectly claiming there is a flaw. Of course I am being sloppy and nontechnical here; I bet there is a subtle, technical sense in which, under reflection, Modus Ponens is more appealing than Appeal To Justin Bieber.