I understand he does not want a literal word count, but that is actually worse. In this scene, he is belittling her for not being able to produce a word count of what he has said- which honestly very few people could- and then the answer he expects to be correct is factually wrong if she truly was able to keep a word count in her head.
This is going to be a repeat of what I said before: his question
isn't meant to be taken literally. When he says, "what words did I say most",
"words" here actually means "what he mentions"-
therefore
factually, the question he is asking is "what did I mention most?"
So no, the answer he is looking for, that isn't a word count, isn't "factually wrong" at all- it is your misinterpretation of his question that is making you think it is. While you're giving that as the reason why you find his ways stupid ( caused by your misunderstanding), I can give you an actual reason why you should find it to be the opposite of stupid.
If you want me to spell it out, that question is a set up for her to realize what caused everything. By telling her about her confidence in her knowledge, he's rooted out the problem of her problems, the source of what is or would land her (and others, because of her) in danger. In vicious high society, ignorant confidence is a dangerous mindset to have as you don't consider possibilities or question what you already know. He proves his point when he reveals the situation she has put her servant in which she didn't think or worry anything about before. At the same time he's saying that that conceited mindset is the catalyst and therefore doubles this as a lesson to her: she's getting someone else in trouble under her orders that she didn't doubt in being a success. If you want me to go into further detail, the writer, by setting up the question about being too confident in one's knowledge, has simultaneously made this so the audience can learn a little more about ML and his experiences.
And I guess you're entitled to compare manhwas with each other, but c'mon. This particular manhwa isn't here to cater to what you like, or do what will make this manhwa as popular as all the other manhwas you named. You're talking about the meme-ish comedy in beware the villainess or the subtlety in the villainess reverses the hourglass as if this manhwa doesn't have its own version of those characteristics. Judging by the titles you named, you're asking for a fantasy level story in an isekai that's doing a more realistic take, it's like you're looking for vegetables in the snack aisle.
Unlike the typical, this one has a realistic heroine who isn't a Mary Sue and whose problems doesn't revolve around being the victim- things don't work out for her or get solved easily- plus the ML is very independent and isn't taking the heroine's side, all of which is rare and different writing for this genre. If you think ML is being arrogant, you're taking things at a superficial level. Instead of thinking that, you should realize what he is actually doing- he's making her think, he's not spoon feeding her, and yes, he's making it hard for her. That isn't what you can call doing things with arrogance. I hope you can appreciate this manhwa somehow, instead of thinking you're above this manhwa's writer.