There isn’t just one particular thing that makes a great photograph, there are many different dimensions and aspects to take into consideration. A great photograph does not have to be perfectly sound in terms of rules and composition to be considered great. Some of the different dimensions of a great photograph are the emotions and/or feelings conveyed, the focus on a particular moment captured, an experience crystalized, a visual narrative created, and so much more. It also allows for discussion, for controversial and hard topics to be brought to light. Like David Griffin said in his TED Talk, photography can be “a positive agent for understanding the challenges and opportunities facing our world today.” There are so many things to keep in mind when it comes to evaluating what makes a great photograph.
I agree that an image is great if it conveys a feeling whether or not it is technically proficient or follows compositional rules.