Jack hates the tone Adam is using when talking to him. It's dismissive in nature and very insulting to Jack's ears.
What does Adam mean by he is not going to learn anything from sparring with him? Isn't Adam's words saying that Jack's not good enough to teach him anything?
This is probably the worst thing one can say to Jack. Jack is arrogant and has immense pride because of his talent. So how can he let some random punk insult him inside his own gym?
"All I hear are excuses? Are you perhaps scared of getting in the ring? Are you about to shit yourself? Do I need to fetch you some diapers?" So Jack immediately starts implying that one tactic which will probably work on almost all men, but not on Adam.
The other gym members who are close to Jack start laughing to make Jack's words feel more humiliating, but it does not affect Adam.
