Can't set featured image

How can I find out what in my theme is interfering with the Feature Images option?

If I select something it never populates, so there’s not even anything to save.

I can active a different theme, then set the featured image, but have to reactivate the original theme again. I set this site up for someone else, and having them have to do that every time is not the most user friendly method, plus they are not the most well-versed in web management either.