The boy's father is like a scarier version of Mr. Banks from Mary Poppins. He's stern, old-fashioned, and the stress of being under financial strain makes him a scary guy when he's angry. In fact, one of the things the boy dreads the most is having his father yell at him.
During the time that this story is taking place, the boy and his father have a kind of truce between them. Even though he's a little disappointed that his son prefers books to football, he buys him a comic book every week, and eats the burnt toast that he doesn't like so it won't go to waste.
When Ursula Monkton shows up, however, the father is seduced by her, and tries to kill the poor boy in his own bathtub. It's way harsh.
The reason that this whole drowning incident is so important is that it leads to huge character growth for the boy. When we first meet him, the scariest thing he can imagine is having his father turn red in the face as he yells at him—but by the end of the story, he's brave enough to ask his father if it makes him feel like a big man to make a little boy cry. That he's says this to a shadow-version of his dad doesn't really matter—he still gathers the gumption to stand up for himself, and that's pretty huge for the little introvert.
So his father's character is a way of showing the huge cojones that the boy grows over the course of our story. And don't worry—eventually it all has a happy ending:
"I finally made friends with my father when I entered my twenties. We had so little in common when I was a boy, and I am certain I had been a disappointment to him. He did not ask for a child with a book, off in its own world. He wanted a son who did what he had done: swam and boxed and played rugby, and drove cars at speed with abandon and joy, but that was not what he had wound up with." (15.40)
While it may take his dad a while to come around to who his son is, we also think the boy deserves mad props for giving him a second chance. After all, the guy does try to drown him, even if ultimately it's only because Ursula makes him.