Everyone has an opinion about everything. I think we can all agree on that. Some people back their opinions with firsthand experience and knowledge about the particular subject that they are criticizing, and some choose to criticize without any.
The first thing that anyone needs to understand about art, music, photography, etc. is that all of it is imperfect. That in itself makes them applicable to criticism. Some criticisms merely point out a different path the photographer might have considered, while some criticisms might point to obvious flaws. Technical deficiencies are the most obvious, and easiest to criticize flaws. People with the most rudimentary experience in photography can tell if an image is out of focus, if the exposure is off, if the contrast is wrong. These are also the things that are the foundations of a technically proficient photograph so before you want people to really get into the depths of the images content, you'd better get the technicals right.
However there comes a point when someone has a deep understanding of the basic technicals of a photograph, that they may choose to break the established rules because the result of that departure supports the content of the image. In the bicycle photo, some people choose to criticize the fact that the cyclist was blurred by motion. To me the whole point is that the cyclist was blurred and personally I would have preferred if he was even more blurred as it would have added even more "life" to the image and would have made for a more visually interesting element. The cyclist was moving after all. In my opinion, an assumption, I would say that those that found the blur of the cyclist to be problematic were most likely novice photographers whose only way to determine merit in an image is purely based on technical and have not gotten past a rudimentary view of photography.
Now breaking the rules does not always work, and unless you know what you're doing can detract from an image. While trying new and different things is key to finding your own style, and for some it can produce work of very high merit, for others it can produce work that many people would find lacking in any merit.
Criticism is key in bettering your work. Criticism from knowledgeable people who can also communicate criticism in a productive way, and more importantly self criticism. Self criticism is ultimately the most important form of criticism. Self criticism teaches you when to aim a camera at something, how to compose it, what affects or techniques can enhance it, etc. And the way you learn self criticism is by criticizing the work of others, and by having others criticize your own work.
Sometimes we get so close to our own work that we lack the perspective to see what we have actually produced. I know sometimes with my own work a certain image I have taken has meaning for me, but I just can't explain why. Quite often others viewing the work, and not being as emotionally involved with it, have the clarity to see what I saw but haven't acknowledged or understood myself beyond a sub conscious level.
One of the things that I was taught very early in my career was to not fall in love with your own work. That you can be blinded by your own ego or by your own insecurities so that you are closed to all criticism of your work. For those often the rationalization for such close mindedness is that you don't want others to influence your work but that rings hollow. If the criticism is valid and true, then wouldn't that be something that you would actually choose for your own work if you simply had been aware of it? Someone coming to an observation about your work before you do doesn't devalue that observation. If the observation is incorrect or inapplicable you are always free to ignore it.
I believe you need to be open to criticism of your work, by yourself and others. But also need to be choosy about which criticisms you take to heart or act on.