A volcano killed the Neanderthals

I did not know that there was a good theory that a volcano wiped out the Neanderthals:

The Phlegraean Fields (Italian: Campi Flegrei) are a series of craters and volcanic areas located near Naples, Italy. ... There’s even archaeological evidence suggesting that a Phlegraean eruption some 37,000 to 39,000 years ago was so massive, it may have killed large segments of the extant Neanderthal population, either directly or by causing a volcanic winter. Now, the massive supervolcano is showing signs of awakening.

I did not know this. All the popular science articles say that the Neanderthals went extinct because they were out-competed by the superior African hominids, who are usually called "modern" and just like today's humans.

No, the African hominids were not modern, and Neanderthals did not go extinct.