You can't just decide that the circle is contained in the set of all ellipses. Anyway its a philosophical argument, you can't "prove" mathematically that circles are ellipses or vica versa.

Why do circles need to be ellipses anyway, why can't they be absolutely different? If they were absolutely different, then circles would be purely ideal, and yet an organizing principle (or as the say in Greek, an ἀρχιτεκτονική, from when we receive the word architecture). The only way to understand this, ontologically, is if we take the world to be in a constant tension with the "earth," as Heidegger puts it (cf. The Origin of the Work of Art), the thing in which the "rifts," which is the actual discourse of idealism, come about.

You know, I thought about it for a moment, and I don't think the visual circle is even universal. The schema of the circle may be, but the circle itself never appears. See this article below[0].

[0]https://en.wikipedia.org/wiki/Molyneux's_problem