I strongly dislike New Testament Bible studies that only focus on part of an epistle rather than the whole; especially in the case of shorter epistles, such as James. But to your question: the Greek de can be either adversative or continuative, and sometimes both. You have to identify which from its context. "Moreover" is an acceptable translation according to Winer's grammar as quoted in the Thayer's Greek Lexicon; but again dependent on context.
As I study James 1:22 in its context, I believe "moreover" fits. In fact that is likely why some translations use the similar connective "and" rather than the adversative "but" to translate the de in this verse, while at least one uses the word "however" for the same purpose. Therefore, given the content of the verse, I believe this "but" in the KJV and other translations can be read as introducing both an explanation of the foregoing and a fresh Idea that flows from the previous Idea. So, if I were translating this I would choose the English "moreover" as likely being the most faithful to the author's thinking as he wrote.
All of what I have said may explain why your study leader chose to end the study at the verse they did while you believe it should continue. In my considered opinion, if they didn't want to study the entire book, they should have ended their particular study with verse 21. I am guessing your study leader, though, felt that verse 22 was a critical part of the thoughts being expressed in the previous verses. Therefore they thought that the "but" was adversative and explained (by contrast) how one should live as a response to what James had just said. So, they felt first 22 finished the thoughts leading up to it. You, on the other hand, feel that the "but" introduces a new idea, which in fact it does-- an idea that is not fully finished until the end of the chapter (verse 27).
Does this help?