There are at least two reasons for Nat's mocking and angry attitude. First, Nat thinks that Kit is engaged to William Ashby, and this makes him feel jealous. In turn, his jealousy makes him unreasonably angry with Kit. Second, Nat thinks Kit is marrying William for his wealth. As a captain's son, Nat likely feels that he comes up short in comparison to William, who is the wealthiest and most eligible bachelor in town.
In truth, Nat has yet to reveal his romantic inclinations to Kit. Afraid of rejection, he chooses to hide his insecurities in mocking and angry behavior.
In chapter 14, Nat sees Kit at the wharf and makes a strange request of her. He asks her to deliver a bolt of cloth to Hannah. For her part, Kit is surprised at Nat's request. After all, she knows that Hannah would appreciate seeing Nat herself. In response, Nat makes a snarky comment about Kit's ability to "spare time" from her "fashionable friends" to do him a favor. Here's the conversation"
"An interesting cargo we had this trip. One item in particular. Sixteen diamond-paned windows ordered from England by one William Ashby. They say he's building a house for his bride. A hoity-toity young lady from Barbados, I hear, and the best is none too good for her. No oiled paper in her windows, no in- deed!" She was taken aback by the biting mockery in his voice. "You might have mentioned it, Kit~" he said, lowering his voice.
"There—there's nothing definite to tell."
"That order looks definite enough."
"May I congratulate you?" he said. "To think I worried about that little bird. I might have known it would gobble up a nice fat partridge in no time."
It's quite clear that Nat feels insecure about how he measures up to a man who can afford "sixteen diamond-paned windows" from England. Also, Nat thinks that William's order proves that he and Kit are engaged. He does not realize that Kit feels ambivalent about marrying William. Sadly, Nat's erroneous hypothesis causes him to treat the woman he loves with mocking anger.