The claim here is about "mulesing", in particular:
That's all well and good that it's in theory supposed to be done under some set of conditions that are not harmful to the animals. But these animals are going to be slaughtered. So as long as that happens, any such processes are simply part of the enablement of further abusing them
As a result, corners will be cut on procedures (like the anesthetic) that we would never want cut for, say, our pets. But this is fine in the mind of the abusers because these aren't beings that deserve any better. There's no point in debating how to treat an animal concerning some procedure when they are going to be slaughtered for meat anyway.
In principle, one could make an argument that they could have a pet sheep and gather wool from the pet just as a fun side project (equivalent to walking the dog or something) and maybe give that wool to friends or sell it. But that isn't the scenario we're in when we go to purchase wool products. Regardless of what exists in some fantasy scenarios, real animals are hurt when you purchase wool products in the real world today.