Interestingly enough, Logan agrees with your assessment of him! At least, based on Logan's in-game actions.
He's abrasive, generally doesn't touch people, and with his now ex-wife leaving him he's a very bitter man, who closes himself off from everyone around him.
Every time you help him out, he notes that you shouldn't.. That you should do what everyone does and tolerate him at best. He tries to do everything by himself, often to the point of severely injuring himself rather than asking for help. Logan honestly seems to believe that he should just be alone, since he's not a good enough person to deserve anyone else - the one person he opened himself up to hurt him really badly.
For me, now, my being kind to Logan in return isn't due to a challenge; it's empathy. I'd like to help Logan trust people a bit more again, and you're rewarded for this by him getting less abrasive. Less angry. Heck, it gets to the point where you can have people meet up with Logan who would definitely have caused him to flip out before - but instead now he just grumbles a little, since he trusts you. Is much more willing to stick his neck out. He's still gruff, since he's stubborn, and you're not going to erase who he is (nor should you!), but I find it heartwarming seeing him open up.
The scene where Logan first transforms, you catch up to him, and he in tears begs for you to stay (since he believes you shouldn't and won't) since he's terrified of being alone /right now/ when he's not sure what is happening to him is one of the most powerful in the game to me.
It's then kind of neat, in my opinion, that Hyao has an option for 'Ehhh I just want a ton of sex scenes' instead, haha, as you can always just go for bottom Logan and get plenty of scenes with none of that 'needing to form a relationship with him' in the way. As really, nobody is for everybody - some people find Caleb being a goofball to be annoying, others rather adore him for it.
Either way, that's Logan for you.