Dad refuses to play with his son because he read somewhere that spending time with his child will lower his testosterone: 'Let him figure out whether child support lowers his testosterone.'

He sounds like the father of the year. 

You don't have to be a deadbeat parent to be a bad parent. Living in the same house as your children, without technically abandoning them, does not make you a good parent. In fact, some would argue that an absent parent should be physically absent. If you're going to ignore your kids, you might as well not do it in front of their faces. 

A lot of dads who aren't present in their kids' lives have a whole lot of excuses for why they are the way they are. They claim that they're too exhausted from work to play with their kids, even though their jobs consist of sitting in an air-conditioned office every day, putzing around on Excel Spreadsheets. They put all of the child-rearing responsibilities on their wife, because after all, she's the mom! It's totally natural for her to be the one who spends all of her time with the children, gets all of the housework done, and works full-time. That's extremely fair and balanced! 

Some absent dads are just plain embarrassed to do what dads do. They're embarrassed to teach their son how to play baseball because he's not automatically great at it, and that makes them feel unmasculine because they're not all that great at baseball either. They don't play dress-up with their daughters, even though it makes them so happy to see their dad wearing clip-on earrings and a crown. They want to do what they want to do when they want to do it, which is not a privilege that most parents have.  If you want to do whatever you want, whenever you want, you aren't ready for kids. 

The dad in this story clearly is not ready for the kid he has, and I doubt he ever will be. A lot of dads have bad excuses for not spending time with their kids, but this one takes the cake.