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).
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.
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.
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.
Also, you can do a lot of woodworking with other tools, like a circular saw, track saw, miter saw, or even a simple hand saw. I've built a couple of bookcases and a built-in storage bench using only circular and hand saws, though a table saw would have made the work easier and probably straighter.
If the safety mechanism failed though, the resulting injury would be far worse as a result of the gloves, so it might not be worth it in that regard.
I'd highly suggest taking a look at some of the videos from Paul Sellers: https://www.youtube.com/user/PaulSellersWoodwork. My first real project was building his simple (but very functional) workbench. He is pretty opinionated so keep that in mind, but he speaks from experience.
Also keep in mind that there are really two "classes" of popular tools: western and Japanese/eastern. If you do get into woodworking I'd suggest trying out a few tools from each class. I ended up going with Japanese saws because they felt more natural to me but then using western style planes.
Unlike Schwarz who I feel like is always trying to get me to buy something else :/
You may want to check out the Bosch ReaXX, which has a similar tech in a portable job-site saw. SawStop is currently suing Bosch for patent infringement (which I don't fault them for; it was them trying to make it illegal to sell saws without their tech that didn't sit right with me).
[1] http://toolguyd.com/sawstops-stephen-gass-people-who-are-des... and a followup that's more balanced: http://toolguyd.com/sawstop-perspective-update/
Don't work alone in the house, keep your cell phone in your pocket. I suppose this would be a great use for Amazon's Alexa, just yell for 911 (does that work for Alexa?).