Because you’re weak and soft.
Wool comes in hundreds of different qualities, some suitable for next to the skin, others better suited to outerwear. For thousands of years, people wore wool – either as fabric or fleece – from swaddling to shroud, with none of this crybabying about thquatching their thoft dewicate thkin. You got used to it, or you scratched.
Nowadays, people haven’t the skill or knowledge to select the right quality of wool for the purpose, and are too precious to give themselves time to get used to wool. They pronounce themselves ‘allergic’ (only a very tiny proportion are allergic to wool; ETA: Claire Jordan reminds me that more people are allergic to lanolin, the oil in sheep’s wool – that one is nasty), and never wear wool again.
Here’s an experiment. Grab a cotton wool ball or a face flannel, and scrub it, dry, over your skin. Or actually look when you’re towelling off after a bath. They all scrape your skin. In the case of the towel, you might well see what looks like dandruff flaking off your body as you dry. You’ll probably need to slap on a load of moisturiser, because the cotton strips the oils off your skin as well, adding to the flakiness.
The only reason cotton “feels” soft, is because the specific cotton fabric in your clothes has been chemically and mechanically treated to feel soft. Untreated cotton sandpapers the top layer of your skin off.