Paulmon's arguments may not be the best, but in his defense, it can be hard to argue in favour of something you don't believe yourself, especially on such short notice. Sure, he doesn't think of himself as a god, but given his position, it's not like he could've publically agreed with Ms. Duxley and let her spread around the idea that all goa'ulds are false gods. And anyway, this discussion was mostly for the benefit of his people, who I imagine weren't taught a lot about critical thinking.
Still, I agree that the semantics do matter, since Paulmon and Ms. Duxley are operating out of different definitions of what a god is. For most of human history, a god was either a pretty alien being with inhuman thought processes (think most nature spirits) or a human noble/king writ large. Such beings were commonly accepted to be powerful (most of the time, but there were also plenty of minor deities who only had power over a single tree, rock or spring and were otherwise on the level of a human except for being unageing), but not all-powerful (and the few that were all-powerful were generally eldritch abominations), and certainly not without flaws. There were many stories about mortals outwitting gods, or besting them at various things, or even about gods being depowered without their magic trinkets, but they were still acknowledged as gods ; hell, gods could even die, and mortals could become gods ! The idea of a single, perfect God (as in, one who exhibits the "four O's" : omnipotence, omnipresence, omniscience and omnibenevolence) is pretty recent when compared to the entire length of human history, and actually fares worse from the perspective of the Problem of Evil, forcing theologians to perform some pretty impressive mental gymnastics, which used to be largely unnecessary for the worshippers of several imperfect deities.
As for the accusation of being a parasite, there is a handy way to deflect it : "Actually, the body you see before you is vat-grown. I made it from a DNA sample, and curtailed its cerebral development so it never developed its own conscience. In other words, it never had a soul of its own and without me in it, it's just a vegetable". A lie, of course, but a plausible one given the capabilities of goa'uld technology, and one that's pretty difficult to disprove.