Parents do stuff just because they can.
This dad discovered that his baby boy is such a sympathetic cutie that he'll cry if his daddy does. Or the baby just wants the attention and Daddy's tears aren't stealing the spotlight? Or crying is basically the main way babies communicate so maybe he thinks they're having a normal conversational back-and-forth?
Let's take it as a sign that we're all born with compassionate natures, which slowly degrade until we're pranking our infants with phony weeping.