In menstrual cycle tracking apps (MCTAs), AI-based predictions and insights have become increasingly popular. These features enable users to receive personalized information about their bodies and mental states. However, there is currently little research on how these predictive AI features and explanations affect users' lived experiences. This paper examines human-AI entanglement in MCTAs through 14 semi-structured user interviews and a group autoethnography. These methods uncover the processes leading to this phenomenon. Our results reveal that: (1) users understand their lived experiences in light of AI predictions, although these predictions can be faulty due to imperfect logging practices, (2) the user interface features and AI explanations do not support awareness or critical engagement with this entanglement and meaning-making, and (3) non-normative MCTA users report a sense of isolation in this entangled interaction. Based on our findings, we propose design implications for predictive AI features and explanations.