Curate, connect, and discover
yohan is Designed to be a morally questionable character. and if the audience is thinking about the context that gaon is given going into his position on the live court show, it makes complete sense that he holds a constant baseline of skepticism for yohan’s morality. from the very beginning, even when unprompted by min jungho, he questions why kang yohan would do things the way he does. the answer he’s given is “politics,” and honestly, if you think about the politicians yohan is surrounded by, the tactics they use, and the willingness yohan consistently shows regarding going to extremes to achieve his ends, it’s no wonder gaon never gains complete trust for yohan. the two of them start off from a place where gaon inherently distrusts yohan. while we can infer that yohan wants gaon’s approval deep down, he doesn’t necessarily prove to gaon that he’s totally trustworthy, nor does he really try or succeed at convincing gaon that there are lines he will not cross, and exceptions where he won’t do the extreme but potentially useful thing for his own benefit.
in any case, gaon does not blindly trust yohan, and this is as much the foundation for the initial success of their relationship (with yohan feeling uncomfortably seen and understood through gaon challenging his words), as it builds up for its ultimate deterioration (gaon suspecting yohan of killing soohyun and accidentally helping in framing him for her death). it’s a very real and human point of conflict between two individuals who obviously care for each other very deeply, but are unsure if they are totally aligned in their morals, values, goals. if anything, it’s a testament to the depth of their frankly-toxic relationship: they want so much to be able to trust each other / be trusted by the other, but being unable to reach that, in the context of surrounding limitations, leads them to (extreme?) behavior that they really don’t exhibit anywhere else. gaon — who has not only heard from others, but also seen first hand, how manipulative yohan can be — is trying very hard to not let himself be fooled, and so he holds extra paranoia and disbelief towards yohan that ends up skewing his judgment. gaon’s not perfect, but he is truly trying his best — especially with the consideration that he’s had it drilled into him by his long-time mentor and father figure that, in this position, he’s got the world on his shoulders.
The reason some people tend to find Gaon's reactions annoying, is because we as the audience always have information that Gaon doesn't.
Granted, we don't always know everything, but even what little what we do know, Gaon does not. Gaon is practically fumbling around in the dark throughout the show.
And when Gaon tries to find out anything, Yohan immediately shuts him down , Soohyun practically babies Gaon and tells him to stay out of trouble and Min Jungho is just a piece of shit.
What are obviously right choices to us is confusing to Gaon because the poor guy does not have all or even a little bit of any information at any point. And if he does, then someone manipulates or emotionally blackmails him into doing what benefits them.
If you look at it from Gaon's perspective the whole show is practically a horror tragedy instead of a thriller (with maybe a few days of peace in between before shit hits the fan. Again.)