The answer to this question can be found in chapter 2 of The Witch of Blackbird Pond. Kit has been consistently surprising people in the early chapters of the book. One of the first big surprises is that she can swim. What's further surprising to Kit is that her ability to swim isn't looked upon favorably. Kit's ability to read is met with an equal amount of surprise from John.
The sequence to look for occurs shortly after Kit describes how the ship was moved along the river through sheer brute force in a process called "walling the river." The sailors are literally dragging the ship one length of rope at a time. It is hot and back-breaking work, and Nat and a few other sailors decide to jump into the river to cool off. Nat teases Kit about it and tries to coax her back into the water. She politely declines and mentions his warning against letting more people see her swim. The two characters flirt for a moment, and then the conversation turns to slavery. It is clear that Kit and Nat are not in agreement about slavery and the slave trade.
Kit is frustrated with the interaction and tries to comfort herself with the knowledge that John at least speaks to her with respect; however, Kit also realizes that John has been equally shocked by her thoughts, actions, and abilities. As an example, readers find out that John was equally amazed at her ability to read as he was with her ability to swim. John goes on to question what she has read and is "incredulous" that she has read history books, poetry books, and even plays. He is especially surprised at her reading of plays, and Kit realizes that John disapproves of her reading choices and is wary of her.
Somehow she felt that John was always drawing back, uneasy at this friendship that was growing between them.