So clearly you're very emotional about this post and I get that, but let's separate a few things.
Your or my view of what constitutes "ridiculous reasoning" is irrelevant. The other day I took a break at work and went downstairs for fresh air. There was a lovely woman next to me having a cigarette. We got talking, and turns out she was a CBSA removals officer. She told me there are people who come to Canadian ports of entry claiming their life is in danger because "someone across the street yelled at me" and that gives them rights under Canadian law to apply for asylum.
Simply because they got yelled at. The reasoning is ridiculous, but then there is the law.
In this case, he is the father of a Canadian child and the husband of a Canadian citizen. I am not saying this is the sole reason he will get to stay, but the best interests of a child are valid reasons for an H&C application. As you said, he has been here half the time w/o authorization and he has admitted to committing a crime. All of that will need to be weighed together by the arbitrators of the various avenues of appeal/asylum claims. He may not succeed, but he has rightly or wrong he has legal rights to make a claim as that is simply the law.
Also, again I get you're emotional as you gave some background, and I didn't say he has been a good father. I merely stated the case may be contingent on if he has been a good father and if he shows remorse and if his wife wants him to stay, because despite what happened, love is complicated.
You say that he hasn't stated "one THING about the condition or support of his spouse" but that doesn't mean it isn't there. Obviously with a situation this complicated and him posting such little detail, his statements/explanations are incomplete. For all we know, she instigated the fight by assaulting him first but he left this out. She could have coerced/manipulated him to stay in Canada without status promising him PR if he has a child with her. We cannot rush to make judgements here because you don't know the full picture.
FYI: I was the victim of false DV allegations from my ex-wife back in my home country. One day we woke up to police reports and legal threats - completely out of the blue. Me and my family had done everything for her: making food she liked every day, driving her around and doing the dishes for her. Total queen treatment. I paid for all our expenses until she could get settled and helped her get a good job. And then, all of a sudden, she left my house and started extorting me. She demanded money, possession of the house I bought, and that I sponsor her brother and parents and pay for their healthcare and education. Literally just like that - like it had all been planned.
So I revoked my sponsorship for her visa before the application was processed and guess what? She got PR, because under the law she could make a whole bunch of unfounded claims. I was never charged by police, but they did come speak to me and looked at my phone, not a single abusive message. It was all normal relationship lovey dovey messages and "what do you want for dinner honey?" The constable was gobsmacked and even said: "I'm sorry to say this, but it's probably a good thing she left you before you had kids. She's a pyscho."
BUT, under the law, the immigration officer in my home country had discretion hear her story, see her crocodile tears and have her visa approved. Ridiculous reasoning. But then there's the law. Remember that.
4 years of my life and close to $100k wasted on a wedding and trips to Maldives and Asia etc. when I could have just married a local, but oh well, I'm in Canada now and life is good.
So I am very, very careful not to make immediate judgements when I see these stories because I see many, many men whose lives have been destroyed. Because like the CBSA agent said, all someone has to do is say "they yelled at me from across the street" and then various instruments of the law give you rights and protections to make your claims.