I can't find it relatable at all, but I can understand why he would behave like that. I can hardly judge this to be a good sign for their relationship, though, unless promptly dealt with. Of course it's still a new relationship, so perhaps he's just not too confident/feeling secure yet, but his desire to monopolise, especially when it comes to Kasane's hobbies (that overlap her job), is pretty bad. But then again, nothing's hopeless because he did immediately recognise he's, himself, behaving incorrectly here. Now I can only hope Kasane won't try to accommodate to his possessiveness too much. That's not the answer to anything, after all. She just needs to make him understand it's not away from him and everything's still cool and the same as far as their relationship goes.
First off, I personally like this arc and I do find it mostly relatable even if it is a rather extreme case here. The overall point gets across, tho.
Same for your comment, I get and even agree with where your thought process ends up at but calling it a "desire to monopolise, especially when it comes to Kasane's hobbies" and then going even further into calling out that she should not "accommodate to his possessiveness too much" is heavily overexaggerated.
This is their first true relationship with infinitely more depth than anything they had to deal with until now as we got to know. They both are incredibly vulnerable by choice which is a good sign. He clearly, known to both of them, is more on the emotional side and more invested into the "usual" relationship aspects- some of it being "my significant other is my number 1 above all"-rose-tinted glasses or sharing everything with each other.
She is more realistic and sees their relationship for what it is, putting it on the same level as work and everything else that is concerning her herself. That in itself is fine and really healthy but this is where this being their first time comes into play- it is all about talking (like is about to happen) and making compromises.
He is kinda trying to monopolise but not possessive at all. He is scared for his place. At her side and in their relationship. She didn't make an effort at all to understand him here (until now) and he didn't communicate properly (as he admitted to himself). He just now realized what I typed before- he is not her sole number 1. She treats everyone the same, which makes her a beautiful human but can be a bit hurtful to a lover. This does happen in other manga, IRL and in other media.
Incredibly well done drama and even if overexaggerated for the medium and entertainment, it flows and feels organic. REALLY looking forward to how this plays out. They both need to make strives to improve as is nature.