I just binged season 1. It's my kind of show so I'm not sure why I was so late to the party. 🙂
I wondered about this, too. It seemed the like the cat plot was just dropped. It looked like it was building to her seeing the cat, but then ants all over the can. So then I was like "did the cat die?" (It was apparently a stray, if not feral, so most likely), and "what was this all about?" Things did go south after that, with more oversight and Holden spiraling, so maybe it was just foreshadowing.
I didn't see Holden as possessive either, but I did see his research changing him. Earlier in the season Tench made a point of asking him how it didn't affect him, and also commented to others how Holden seemed not as affected. I think this showed he really was affected, and more than just getting a big head about the work.
I also saw that Debbie and Patrick were doing more than talking in that dark room. I saw her sitting on the table, and I thought he was standing between her legs when the lights went on and she jumped up going after Holden.
That said, I never thought they were a good match and didn't know how they stayed together so long. And it's not like I didn't like her - I liked that she was smart and independent and had no problem speaking her mind. I just thought they didn't make sense as a couple. She always seems slightly annoyed by him, or slightly looked down on him. It was more like she tolerated him. And he definitely has flaws, big ones, but I don't think it made sense for her to be in a relationship with someone she felt that way about.
I had more thoughts on other things, but I'm starting season 2 now. 😄