Would you be okay if your boyfriend wants to do bible study with someone who is interested in him?

He told me two weeks ago this woman expressed interest in him. He used to talk to her before me casually as a person of faith, and all of a sudden she popped back up asking if he has someone. , Today she shared a song with him. He then asked me if he could do bible study with her seeing she has questions. It caused him to get alarmed when i told him i needed to think, called off my phone and thought i was going to break up with him. He gave me the impression he wasn't going talking to anyone but ...
He did share " some" of their conversation with me and tried to pass it off that she has someone she us interested in. But why would he even continue talking to her? And then now wants to do bible study