I finally know what to recommend to those people who keep asking me for something like Oyasumi Punpun, because these are the only two things I've read which make me feel sick and I've read a ton of edgy, gore and violent mangas.
I'd split this manga into two sub-thematics, but the general idea is about despair in my eyes. First, there's a salaryman whose wife is dead and his daughter is a shut-in who refuses to even talk to him. He leads an horrible life focused on a job he doesn't enjoy and which is tiring him out, and essentially he's getting targeted by his coworkers who are jealous and try to ruin his career. Any white collar worker would recognise the pain this guy must be feeling.
So how does he solve his problems? By getting manipulated into a toxic (and illegal) relationship with a minor. This works tries to focus on that, but this is where it fails because it ultimately doesn't give any sort of message. Is it trying to defend or criticise something? Hard to say. It does a good job at showing how desperate the protagonist is and how everything around him snowballs into an ever worse situation. The relationship he clings to, you can feel how bad it is for him and how it's not supposed to be a solution, neither for him nor the girl. You don't solve a teenage's family problems by dating them and you don't solve yours by entering into an illegal relationship which is going to bring downfall on your head the day you're caught.
It could have been just that, if it didn't seem to try to defend the idea that their relationship is legitimate. The heroine is essentially manipulative and toxic at first, but then she gets shown in too much of a good light which breaks the cohesion. The author wants to excuse her behaviour too much by showing that she has had an hard life too, I think he wanted to describe a father complex but that is never clearly explained as instead we see an unhealthy attachment to her mother and a "puppet complex". Then the protagonist's legal problems are somehow magically forgotten, and there's no proper conclusion of any sort anyhow, be it a bad or happy (them breaking apart and trying to repair their lives on their own) ending. I'm honestly disappointed all the societal problems were thrown aside, I think it would have been much more interesting than the rest of the manga and it fits into the idea of all the despair that had been shown throughout the manga, what better way to continue on the same thematic than having the protagonist faces the consequences of an illegal and immoral relationship?
It also has the same problem as Punpun: a lot if not all characters are absolute assholes/insane. I think that was not the intention of the author, but the protagonist's girl is shown as such a selfish person it is unbelievable how hard he tries to be a good father.