In short: Before the Ptolemaic system, it was assumed the planets moved in circular orbits around the earth. The problem is, this did not explain the phenomenon of "retrograde motion", which is when a planet apparently slows down and moves backwards in its path over the sky, as observed from the earth. Ptolemaus added the epicycles which describes the planets as additionally moving in smaller orbits along the path - just as the moon moves in a smaller circle around the earth, which would result in retrograde motion if observed from the sun. In other words, the epicycles explained a phenomenon and allowed the model to better predict the future movements of the planets.

The thing is, this model is not wrong and makes reasonable correct predictions about the motion of the planets as observed from the earth. The Copernican model is just simpler because by describing the planets as orbiting the sun rather than the earth, you don't need as many epicycles in the model. The Tychonian model, by the way, solves the same issue by having the planets orbit the sun, but the sun oribiting the earth, thereby additionally solving the parallax problem which the Copernican model could not explain given the knowledge at the time. All three models needed additional epicycles, which Kepler simplified by describing the orbit as a elliptical.

You will note these models are actually equivalent in modern understanding, where neither the sun or the earth is at the center of the universe.

The current model of the solar system still have epicycles (eg. for moons), so if the presence of epicycles somehow turns a model into pseudoscience, then what?