@gronkle There are a few things that don't convince me of your argument.
1. The mother's attention is caught the instant the father says it, which the story has consistently used as a signal that this is the perception being challenged. This is meant for us as readers to pick up that "men don't get scared" is the problematic view being addressed, and whether or not it's being used as a motivator to help Hiroki conquer fear is irrelevant to the story.
2. Your argument ignores the numerous times Hiroki's father pushed heteronormative values onto his son throughout the story so far. He means well, and it's not wholly his fault that it makes Hiroki uncomfortable, but the problem is that his perception of manhood is narrow. He indirectly shames Hiroki for being okay with a homosexual kiss on television (chapter 7), pressures him to be more proactive towards getting a girlfriend (chapters 9 and 10), and tells him boys can't have crushes on other boys (chapter 14). Based on that history, it's not illogical to conclude that the father's behavior in this chapter would be similarly motivated.
3. The whole point of the chapter is to show that it's okay for a man to be scared, not for Hiroki to overcome his fear. His immediate counter-challenge is not primarily meant to be a bonding moment (even if it's the end result); it's a demonstration of confidence in his own manliness and a teaching moment for his father to open up to different definitions of manliness. It takes the perception that men don't get scared and flips it on its head. Yes, Hiroki overcomes fear afterwards, but it's only because he sees a buff dude in danger and that's the joke.