We know that chometz symbolizes avoda zara (as the rishonim explain, that one of the reasons that chometz is ossur even if it is only a mashehu, a tiny amount, is because chometz represents avoda zara, in which even a mashehu is forbidden, ולא ידבק בידך מאומה מן החרם). And the above idea is true with regards to avoda zara as well:
Every aveiro in the Torah deals with a certain existing object (whether a food (such as bossor becholov, cheilev, dom etc.) or a plant (such as kilaim, orloh etc.) or otherwise), about which the Torah gives specific directives about how we may or may not interact with it (not to eat, not to have any benefit etc.). In all of these cases, the dovor ho’ossur, the meat mixed with milk, the non-kosher food and so on, is a real (halachik) existence, that results in specific halochos that govern how we behave with it.
But avoda zara is very different. An “Elokim acherim” is not a real existence, it’s something that doesn’t and can’t exist. The mere notion of an other G-d ch”v is the most unexistable concept in existence!
So, it’s not that avoda zara exists, and Torah tells how we may or may not interact with it. Rather, with avoda zara the point of the mitzvah is to govern our mindset, the aveiro of avoda zara is for us to think about it as an existence. The expectation of Torah, with this mitzvah, is that our mindset should conform with the view of Torah, with the truth, that 'ה הוא האלקים בשמים ממעל ועל הארץ מתחת אין עוד. We fulfill this mitzvah by recognizing and acknowledging in our own mind that there isn’t – and can’t be – any avoda zara to begin with!
