Our cat used to eat moths. She used to sit in the window when it was sunny and sunbathe. The sun, of course, attracted the moths and other flying creatures. She would occasionally catch some of them. I do not believe that she made very much effort to do so though. I think she only ate them if they happened to fly very close to her. When they did that, she would just turn her head around and snatch them out of the air. My dad saw her do it a few times. We think she did not like the taste of it much because as she chewed them she would screw up her face and seem slightly disgusted. She probably just did it out of instinct: we were feeding her sufficiently so she was probably not really hungry. Perhaps she only ate the ones that had irritated her by flying so near to her. She was a rather fussy eater anyway and if we tried to give her the same thing too many times, she would stop eating it. We had to give her something different then and we could only give her the thing she had stopped eating after a few weeks of other foods.