It appears to me that the differences System 1 and System 2 reasoning be used as leverage to change one’s mind.
For example, I am rather risk-averse and sometimes find myself unwilling to take a relatively minor risk (even if I think that doing that would be in line with my values). If that happens, I point out to myself that I already take comparable risks which my System 1 doesn’t perceive as risks because I’m acclimated to these—such as navigating road traffic. That seems to confirm to System 1 the idea of “taking a minor risk for a good reason is no big deal”.
I think some behaviors which may be considered arrogant can be justified. For example, dismissing other people’s opinions out of hand can be a good choice when actually surrounded by people with very low-quality opinions.
As for appearing arrogant to others—it may be a difficult-to-avoid side effect, or it may have value of its own—there are social contexts where acting arrogant is useful.
Is it arrogant for HPJEV to consider himself to know better than the adults around him? Maybe so, but he’s right about a lot of these things. (I believe there’s a significant subset of HPMOR would-be readers who found Harry insufferably arrogant. Does that mean he should change his behavior?)
Having tabooed “arrogance”, one of the interpretations is “emotional attachment to the idea of one being right”. That, I think is a real problem for an aspiring rationalist—you need to be able to consider the possibility of being wrong.
As DanielLC says, you should calibrate yourself and neither strive to underestimate nor overestimate your abilities.
(If they aren’t well-calibrated, that seems like a likely outcome.) Edit: not sure about this part.