When we talk about "turning away" from something, it often suggests a feeling of reluctance or rejection. There are plenty of synonyms that we can use to describe this state of mind. For instance, we could say that someone is "averting" their gaze or "avoiding" a specific situation or person. Alternatively, we might talk about someone "withdrawing" from an interaction or "resisting" a particular idea or proposal. "Ignoring" or "dismissing" something are also valid ways to convey a person's "turning away" from it. Ultimately, it all depends on the context and the specific nuances involved in the situation.