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This goes beyond "show you sources" to "you need classes in genetics, microbiology, organic evolution, and maybe statistics". For what it's worth, I'm an educated and experienced microbiologist with experience in public health. I'm not sure how to cite what's effectively a semester of college education and four textbooks into one comment. I can explain the basics and you can verify details if you'd like. I am more than happy to answer questions and point you towards where you might find more information on specific topics but citations for all of this would be a huge endeavor.

There are two main reasons H5N1 isn't human-to-human: specificity and, by its effect, low transmission. I'll try to keep this super high level.

Regarding specificity, viruses don't infect cells at random. Instead, there's basically a "lock and key" effect where the virus attaches to an external component (receptor) of the soon-to-be infected cell, then it releases its genetic payload. Much like how it's pretty easy to pick most locks, it doesn't need to be a perfect match, just close enough to get the job done.

This is how you get some splash over between species, as there's variation in both the virus and potential receptors due to mutation, and through random chance you might get a good enough match. The more exposure a virus has to potential receptors, the more likely it is that this will happen. If it happens, the particular mutation making this possible will be selected for in that individual or population, creating many more copies of a mutation that otherwise may have just died out. This is exactly what happens when a human gets infected with a zoonotic virus.

Next we have transmission. Not all cells in the human body have the same receptors, so viruses can infect different parts of the body. This is partly why people get "head colds" and "stomach bugs" - that's the region with the most cells with the target receptor. H5N1 isn't particularly good at infecting human airway cells, so infected humans are fairly well dead ends as this blocks airborne transmission, its primary mode of spread.

Currently, H5N1 is one point mutation, vastly the most common type of mutation, away from switching specificity to humans and infecting our airways. This is incredibly small and viruses churn out point mutations like crazy. Every time some dingus swills down raw milk, we're rolling evolution's random chance mutation dice. If just one virion has that single mutation and successfully infects that moron's airway, it's game on for a potential new pandemic. Evolution is just a numbers game and the more chances you give it, the more likely it is to happen.