Actually, I really like this premise. A seriously depressed, broken down man with mental issues that feels dejected by society. He tries to keep it in check but he feels so out of place and so lost to human contact that he can't pull himself through and so tries to manage as he is.
To address some stuff:
Do you remember the central metaphor? She said she saw him as a "wounded beast." What do animals do when they're in pain? They don't let you help them and they bite and slash back at you. She probably views him as a sick man who needs help more than as a predator or as a criminal, which from what we see, he is. Also where I live, you see couches outdoors all the time as people just dump them, but I suppose it could be symbolic for counseling/therapy instead of a literal thing. Though I will give credit to the idea it's all dream-like sequence as its framed that way with him being alone aside from her and them being quite the ways away.
@Askorti @Xxjuggernaut
The first chapter may not be funny, but that might not be representative of the manga as a whole. We do see a joke when she's giving him a lap pillow, though.
@Fellow_Weeb @migh