The most obvious example of this, of course, is his very strong need to not notice that Elly feels stifled being a housewife because she fears that she doesn't have an identity of her own; there are times when I think that part of him actually seems to want to believe that Elly can't have an independent identity owing to a lack of a Y chromosome but most of me believes that he's a lazy, stupid fool who'd rather make inane jokes about hormones rather than face the fact that he might just be a creep.
His inability to be there emotionally for his family also explains why his solution for Lizzie's habit of sucking her thumb was not something scary and impractical like acknowledging the fact that she felt like she didn't fit in or taking her cretinous bully of an older brother aside and offering him a big glass of "Get over yourself, Moron"; his wonderful, jolly solution was to stick a piece of hardware in her teeth that made her sound funny and feel worse. Since he's an idiot who won't admit that his ideas never work, he blamed everyone but himself for the collapse of Operation: Orthodontia.
The nadir of his refusal to do anything difficult for his family, of course, was the Housening; since finding out what was bothering April or telling his entitled clodhopper of a son to get off his lazy rump and get his own pad yesterday was too much like work, it was better for him to stand around like a shivering pillar of shite talking about how he couldn't control Mike and making swinish comments about the spoiled princess he didn't know he raised.
That being said, there is one way one can get John to do something: make sure it furthers his agenda to own horses because he thought that small children who, depsite the fact that they could not survive on their own no matter what he thought, were bumming money off of him. It worked like gangbusters three years ago.