There is a time and place for sharp images where the action is frozen by a fast shutter speed. With the advent of ultra-fast ISO digital sensors, it is easier than ever to shoot that way.
But sometimes a slow shutter with a bit of blur tells a nice story in an abstract way that the “everything sharp” approach cannot.
It takes practice to know how slow the shutter needs to go and how to “pan” along with the subject as the mirror is closed during the exposure. You want the image to show some motion but not so much that the head, legs or wings totally disappear. Usually the key is in the eyes of the subject – if you can keep they eye somewhat sharp while the rest of the image blurs, the image has a better chance of “working” artistically.
There is a low success rate, too. You might have to shoot twenty images just to get one you like. (And when you get one you like, you might show it to your spouse, who then looks at you like you are crazy and says “meh” because she doesn’t like images that aren’t sharp – which goes to show you can’t please everyone, all the time).
Black bear abstract, Northwest Trek Wildlife Park, Washington, USA (captive). Canon 1N RS. Fuji Velvia.