It seems to suggest that no self employed person adds anything to the economy, supports an business in any sector, is of any Earthly use to anyone.
No, that is exactly missing missing my point, which is that funding is nothing to do with the worthiness of individuals or the general economic usefulness of their contribution.
99% of self-employed will essentially be selling their labour, like employees. A period without sales revenue won't cause them to go out of business forever. This is in contrast to a large business with hundreds of employees, making payments of hundreds of thousands a month on property leases and capital equipment financing, who if they go bust will be out of business forever, the equipment sold off for next to nothing or possibly scrapped, the buildings recycled to some other purpose. It's these more complex businesses that the furlough scheme wants to keep alive.
A tradesman with a van and some tools might, at worst, lose his van. But that's not going to stop him restarting his business in normal times, so his business doesn't warrant the same kind of extraordinary intervention. (Reiterating, furlough is not there so individuals are looked after, it's there so businesses still exist when normal times return.)
It doesn't help people's confusion that the government (understandably) doesn't turn down all the credit it gets from furloughed workers, even though helping them is a means to an end and not an end in itself.