Jason is very arrogant and interested in maintaining his reputation of a hero. He doesn't want Circe to think that he didn’t complete the challenge fairly, which would suggest that he wasn't talented or strong or impressive enough to beat Aeëtes's test. Medea wants to protect his pride, which she does by telling Circe a story that makes Medea look weak and love-struck. By saying that she begged Jason to do as she suggested, it seems like he was helping
her instead of the other way around. This way, it appears that Jason has more power in the situation, even though it is actually Medea who, with her magical powers, passed Aeëtes's test. She, not Jason, is the reason why his quest succeeded.