“fur clothing” means that the fur is still attached to the skin, regular wool products are shaved from the sheep which is about as traumatic as forcing a grumpy teenager to take a shower.
The problem is that commercial sheep farms compete for the lowest price, which means that those who actually care for the welfare of their animals are at an disadvantage to those who keep sheep in very bad conditions, and will be forced out of the market sooner or later. Customers and distributors usually have no clue how the animals were actually treated, they just see the price and choose the lowest, of course.
And while you might not need to kill the sheep to get the wool, they’re killed when their “productiveness” drops below profitablity anyways. In the wool industry that’s after about 5-7 years.
Just because such animal products could theoretically be produced in a humane way, that’s not what happens in practice under capitalism. The vulnerable are always exploited as much as possible for financial interests and animals have no voice, no lobby and no lawyers.