You can stay calm that it is for free, yes
there are several lines in the MCs thoughts where he clearly explains why he's doing what he's doing - it is a bluff, she knows it's a bluff. That doesn't really matter in the end, because it serves its purpose - to make her remind herself who she is and what kind of a person she is. For the same reason it's intentional that he repeats himself - picture it this way, if someone is very insecure, degenerate and well aware of his own issues, do you need to convince him what kind of a person he is? Or do you need to make him think about it and come to his own conclusions?
As regards the "losing his cool", MC is human. You're human. You lose your cool, so does he. I'm personally not a fan of the all-powerful, all-knowing, always cool, always beats everyone up and wins everything guy. He has flaws and it's been established arrogance is probably his biggest flaw - you as the MC, if you were in his position of the golden CEO of one of the most valuable companies in the world, you'd probably have developed some very flawed arrogance as well. Now imagine if the person you probably least respect and consider the weakest suddenly destroyed you and your entire life. You wouldn't lose your cool? And yes, Melissa never shuts the F up. That's mentioned multiple times. The smallest dogs bark the loudest
Yes, a lot of this would probably be better if there was a very long scene explaining his thought process and additional things it'd heavily break the pace of the game if there was a very long thought scene explaining it from A to Z. One of the biggest complaints was that the whole sequence of events there, with breaking Melissa, was way too long. So...
Anyway, it's unfortuante people don't really like the dialogue and the update. Personally I'm very critical to myself and I liked it because it really shortened a lot of that bloat there that made the scene drag on a little and I don't feel a drastic change in the MCs behavior - but of course I'm not the most objective judge