I am not a doctor and I am not a specialist in hyperbaric medicine. This reply is based on Deco for Divers. It is possible that I have misunderstood something. If so, please correct me.
My answer:
1. Because on ascent nitrogen gas can enter the microbubbles that naturally exist in your blood stream...
(any fast flowing liquid will have bubbles:
Cavitation - Wikipedia)
2. And these microbubbles will grow not just on ascent but also by offgassing...
(the surface tension of the bubbles must be overcome, which means no bubble growth from offgassing will happen if your dive is 1.6 ATA or six meters or 18 feet deep only; the pressure change however has its effect, but that is not a problem, because excessive growth cannot happen)
3. And be filtered in the lungs...
4. But if they get re-compressed and small, they can avoid that, and get through, and remain in blood stream for longer (=simply more bubbles), and cause trouble somewhere (eg. block blood flow in the skin = skin problems or block blood flow in the brain = neurological DCI). This is why yo-yo-profiles are bad.
Hence, I believe that it is not only the dissolved gas that kills you. It's also your up-down-up-down-movement. There are actual scientific papers that list yo-yo -profiles as a risk (see figure 2):
https://www.dhmjournal.com/images/IndividArticles/49Dec/Lundell_DCIFinland_2019-42(564).pdf
ps. If the Buhlmann algorithm alone would be enough (supersaturation alone leads to trouble), then only the drop in pressure would be relevant, not any back-and-forth motion, because sinking would make gas dissolve and cancel bad things, would it not? Pehaps the bubble models just need work?