Why vegans don't support wool

I recently was doing some reading to remind myself of why vegans don't buy/wear wool. A quick summary which I sent to the friend who I had been discussing this with:

• Vegans are against exploitation of animals. Veganism is an economic boycott against industries that profit from animal exploitation (which most often involves animal suffering + premature death).
• A common counterargument is that sheep need to be sheared anyway, so it's not a problem for us to keep doing it. But the reason they need to be sheared is because humans have selectively bred them to produce more wool than they can handle on their own, and so are now dependent on us to shear them.
• Mutilation of sheep is a common practice, eg holes punched in ears, tails cut, castration, carving flesh from their hind so they don't get piss on their wool
• The sheep are slaughtered once no longer productive.