Felling trees can be dangerous but, the chainsaw saw? With care, the right clothes,chainsaw resistant overalls, helmet, correct footwear, mask and safety glasses, respect for and knowledge of how to correctly approach the job at hand, the saw isn't particularly dangerous.
Establishing and cleaning up escape routes. Boring the tree to find if it's solid or diseased is required in some instances. Did the tree spiral as it grew? It might just explode, twisting and spinning, the cut is started.The helmet is for falling objects you didn't see on inspection. Don't forget to use your ears, listen to and pay a bit of attention to the tree as you cut or drive a wedge. Having a watching assistant or, at least a listener close by is good safety practice. Cell phone always handy if no assistant, maybe you'll be able to use it if required.
Stab cuts, rip sawing, and such need practice but a sharp saw, correctly used isn't particularly dangerous. Weekenders with saws? Well, yes there will be an increased danger. Usually only one avoidable accident and the chainsaw is history though. Most people are reluctant to suffer a second accident. Even the most ignorant/lazy usually learn the first time the loop takes a bite of thigh or jumps nearly to their face when applied incorrectly to a tree/limb/body. Chainsaws are hard taskmasters.
Chainsaw manufacturers have some great videos all neophytes or returning drivers should review.