The content of what he has said is nasty, whether he said it calmly, through gritted teeth, tears or screamed it at the top of his lungs.
‘My partner has made it clear he hates coming home after work, and was particularly vocal about his feelings tonight.’
This, and other sentences suggest this is not a one off - ‘hateS’ i.e. not a one off - ‘particularly vocal’ i.e. has been vocal before. This is where I got repeatedly from.
Its not a huge leap to say that someone who openly says they hate coming home and spending time with their child hates being a parent and what it entails.
She’s said specifically a number of negative comments that he’s made. Maybe he has said ones along the lines of ‘Christ I’m not coping’ as you suggest, but I’m going on what she’s shared here so far.
He hasn’t explicitly said he wants her to solve his problems but what is she actually supposed to do with this information? Say ‘ok, dear’ and crack on with making dinner like he’s not said all this horrible stuff?
He’s complained repeatedly about (what he perceives as) problem after problem - a running commentary of everything he hates but is doing nothing about it.
At what point does he need to take ownership of the fact he hates everything and do something about it?
I am not unempathetic about someone struggling with parenting or life but that person does have to take some responsibility for trying to help themselves and how they can manage to live with a situation they created, without verbally lashing out at those around them.
I can see you’re trying to give her partner the benefit of the doubt - and yes it sounds like he is finding is finding things tough but finding parenting hard isn’t a get out of jail free card to being horrible to your family.