We saw enough of the El-Aurians in Generations to know that, although extremely long-lived & intelligent, they were flesh-and-blood mortal creatures. Tolian Soran & Guinan were both refugees, caught in the Nexus, having fled the decimation of their civilisation by the Borg. So the image of Q – an omnipotent, god-like creature – apparently scared of Guinan, was intriguing. It remained an enduring mystery for decades, until Picard season 2.
In Picard, we learn from Young Guinan that the El-Aurians and the Q had a ‘cold war’ which they eventually settled. Why they had this war isn’t fully explained, nor is how a mortal species had a cold war with a species that could simply blink them out of existence with a click explained either.
What we DO know is that El-Aurians either had or gained the power to ‘summon’ Q at will. So a possible explanation is that the “time sensitivity” we know the El-Aurians have was constantly being rattled by the Q who were stomping around meddling with time with reckless abandon. The El-Aurians began summoning Q and telling them to knock it off because the changing timelines were driving them mad. Eventually, the Q relented and agreed to stop pissing around with Time, but some were more reluctant than others. Perhaps ‘our’ Q was a hold-out, and Guinan was one of the more militant El-Aurians, constantly summoning him (which would be kind of annoying). Young Guinan does explain that some Q aren’t actually that bad (implying our Q is).
It still doesn’t quite explain Guinan’s cat-like pose when she encounters Q on Ten Forward [which I think was an improv by Whoopi Goldberg], but her ability to summon him whenever she wished, and the fact she could summon other Q to grass him up for breaking the El-Aurian-Q truce, could be interpreted by Q as a valid threat.
This is one of the more fun aspects of Star Trek. A throw-away scene in an episode, in which the scriptwriters were just trying to drum up a bit of fun and probably thought little of it, ends up being one of the most enduring mysteries of the show, spawning its own fan theories, and eventually being (sort of) closed off in canon much later.