Chemical biology Phd, did work on (non-pathogenic) gain of function research here.

1. We care about a furin cleavage site, because it sticks out like a sore thumb. It doesn't exist in the closest family of coronaviruses to SARS-COV-19, yet exists in distant relatives. This is the exact sort of thing you fuck around with if you are doing GOF (pathogenic or otherwise) research -- you know it's likely to be tolerated by the parent scaffold because relatives feature it and aren't completely unstable -- and you see the vague outlines of a correlation with function.

Furin cleavage sites are also something a bioengineers like to engineer because we are familiar with them (we often create furin cleavage sites for protein production -- to liberate the purified protein from whatever scaffolding we use to build the protein -- or for analytical purposes, because you can get good evidence that you built what you built if it gets chopped in two).

Finally, we know that a nonprofit associated with the Wuhan Institute of Virology proposed specifically to engineer furin cleavage sites into coronaviruses (in association with WIV, but with the research done in the US), which proposal was rejected by DARPA.

2. HIV doesn't have anything to do with anything except that this is what the protein sequence of the spike matches up with. This is ~6 amino acids, which is admittedly not a whole lot, but not all furin cleavage sites look alike. If I am reading this blogpost correctly, the HIV-1 DNA sequence (which can represent the same protein sequence with worst case ~60% divergence) doesn't match up with the coronavirus, but the moderna patent sequence does (and it's exact). The moderna patent furin cleavage sequence known to be based on the HIV-1 sequence.

3. You ignore those results because NCBI will send you a hell of a lot of COV-19 sequences, because guess what, we've been sequencing the shit out of COV-19. But your criticism of the "statistics" that come out is 100% correct. It's possible that in the last two years have found a "missing link" that will be filtered out by those criteria, though one suspects that if such a thing were found, it would have made some pretty big headlines.

So, if we do a dispassionate analysis without considering faulty application statistics to the pre-2020-only sequence counts, and simply sticking to the existence or inexistence of sequences as per the database we are left with a few possibilities:

1.

COV-19 precursor protein intermixed with HIV-1 and did an uptake of the DNA (this is totally possible but rather rare, even given that HIV-1 is rampant in the wuhan-ish part of the world), then somehow converged on the moderna sequence (let's say 1 in 250 odds).

2.

Some (prior-to-2020 unknown or unregistered) DNA sequence that happens to exactly match up the moderna sequence, by chance, got merged with some wild Coronavirus sequence to yield covid-19.

3.

- someone came up with the idea of fusing furin into coronaviruses (true if you believe the leaked DARPA grant application, btw I have read the whole thing and the level of detail and its similitude to grants I have read and written would have been really hard, but not impossible, to fake, especially by a state actor.)

- someone went ahead and did the research on a slightly different coronavirus than proposed in the DARPA leak even without grant money (this does happen in biology, I'm probably on the tail end of the distribution but out of 10 years in science only 1 was working on previously proposed research, the other 9 were on research I was gathering preliminaries for to write grants)

- the postdoc or grad student assigned to this went and collected a bunch of furin cleavage sites, probably off of NCBI blast, and stack-overflow-copy-pasted them into the coronavirus, of which one was the site from the moderna patent.

- the moderna sequence randomly happened to be the "winner" and spread around.

4.

Moderna engineered covid-19. (I don't believe this, but I included it for completeness, because I don't have a good intuition of why I don't believe this)

I don't know what the statistics on 1 and 2 are, but my gut feeling says they are rare. But rare things happen, and we cannot discount that, and there is a bias to see things that look good. We can't say "it's too good of a coincidence that the furin cleavage site happened to be in the right spot" -- because those events are selected for by the results. For 3, it's bullets 3 and 4 we don't have particularly good priors on, but I think it is extremely irresponsible to claim "it could never have happened", because they are things that I would have done if I were given the directive to insert furin sites into coronavirus. My gut feeling, thus, is that 3 is the most likely, due to projection: I assume WIV researchers are as smart (and as dumb) as I was.