Powertools are made to cut/grind/drill/etc... wood, metal, and even stone into useful shapes. All of these things are significantly harder than the human body. Of course the tools capable of doing it are dangerous.
For example, you wouldn't want to wear loose or baggy clothing around a lathe.
Also, when I was a kid, my Dad had almost lost the tip of his finger in a snow blower -- he was cleaning out the chute when his glove caught on the blade. Again, something that you aren't supposed to do. For myself, I've had a number of close calls -- sometimes a piece of wood gets ejected in the direction of the blade spin. I've learned to stand to the side, and now directly in front of the saw. Also learned the hard way that you don't support a board on both ends, and cut in the middle with a circular saw -- blade pinch, and a nasty bruise results. Again, if I had someone standing there that could warn me, I would have corrected my technique before getting hurt.
i had a roommate for years, was a very skilled machinist... we called him "nine and a half" although he was really only missing about 2mm from his right index finger... state compensated him $10k for those 2mm's though.
Common errors are things like trying to cut a piece that is too large / awkward, resulting in the wood pinching the blade, and also getting your fingers too close to the blade. Get used to using push sticks to push the wood piece through. Typically you'd make up a couple of them with notches in the ends, or with a rubber tip. If you are doing certain types of cross cuts, the table saw has a couple tracks and a jig that runs along them, to move the piece through. Also, most important, is to set the blade height correctly, so not much of the blade is sticking out through your work piece.
Of course, I've always wanted a computerized setup, where you specify where the cut should be, and the work piece gets robotically placed on the table saw and precision cut. (they have this in some of the larger cabinet shops).