Hmm there are certain couples that you just want to protect and support this is more of an anime visual novel and anime ofc which would be Steins; Gate, the couple there is just so perfect QuQ they complement each other well and like one character makes the other be the best version of themselves.
First of all, I like paying close attention to their dynamic before they are an actual couple. I don't like the romance until after the story makes me care about them, when I know their motivations and their interests, also watching how their relationship as acquaintances or friends develops and see the 'chemistry' between them.
Sometimes I see the chemistry elsewhere and end up shipping BL or GL because of how the authors described their dynamic, I know this isn't what you asked about but it's important to mention since if the main couple is boring or just forced together, it will motivate people to ship them with any other character.
In my case, the couple in steins; gate is so perfect for each other that I don't dare pair them with another character :0
By the way, you said you wanted to pinpoint exactly what makes you feel that way about some couples but you didn't explain that xD I'm curious on what makes you feel that way so do elaborate!
Personally, I like it when I'm not expecting the couple to happen, when you just start reading something and you don't think anything about them but that when through seeing them interact with each other... The story motivates you to like them together. If the romance starts from the beginning it has a high chance of me not being that much interested, though, it can start as a crush and be okay anyway, but at least be one sided for the time being.
I like slow burn stories, so, I need reasons to pair someone with another! GL isn't my favorite, but I've happened to think two female characters make sense together because of how they were written, so yes, it depends a lot on how the story presents them.
One example of cute couples I support from comics is from 'Who made me a princess' with the main girl and Lucas, I simply liked the dynamic between them as it was way more natural than the other boy that likes her and you see, the main and Lucas weren't interested in each other at the beginning, so I think it is the slow burn and how they get to know each other.
Haha it's a bit hard to describe everything I feel from couples but I don't know it's this inner feeling of omg they care for each other even when act like they don't xD and I don't mean tsunderes necessarily, cause those are often exaggerated.
I just really like the progression and seeing characters care in their own ways, it's really cute xD Seeing the subtle signs is really satisfying, more than seeing clear romantic intentions from the beginning.
Lol sorry for the long text, but hope what I said made sense somehow xD