All animal products are not vegan with the caveat that you live in a modern society. The fact that we do have the ability to go to a supermarket and choose what food we want to eat, what clothes we wear, etc means that turning those animals and their products like wool into commodities for our own use is inherently not vegan. The definition of veganism includes this caveat by way of the phrase "as far as is possible and practicable" (https://www.vegansociety.com/go-vegan/definition-veganism).
So if you are an Eskimo and you literally have no way to survive other than killing an animal or using it's fat for warmth, etc that could be considered vegan. Or at the very least, I don't think that anyone including vegans would argue that that person has a moral obligation to simply let themselves die. However, the vast majority of people that ask questions like this are not in a situation like that. We really don't have to wear wool or eat meat or drink milk. So by doing it when it isn't necessary you are inherently causing unnecessary suffering which isn't vegan.
And to be clear, animals like sheep produce wool for a reason. When we take it from them and view them/their wool as a commodity we are already crossing a line. It would be easy to see how keeping human females locked up, breeding them to produce more and more hair, and taking their hair to sell to make wigs would be unethical right? You are taking away their autonomy even under the best conditions. If that individual was able to consent and they signed a contract that gave them food, shelter, water, and whatever else the needed in exchange for their hair that would be another thing, but sheep can't consent. Capitalism will always lead to farmers treating animals as commodities and not as living beings.