I think the premise is wrong: in physics "everything is similar" unless proven otherwise. It's one of the principles of physics.
So you say that the orbit (shape? Or did you mean velocity, or something else) should't be "similar": but in what way should't it be similar? You should specify that, what did you expect?
If your premise is: "the velocity at perigee is much higher than the apogee, so how can the curvature be equal and form an ellipse".
If that is the real question we can look at Kepler's first law, and/or second law (again based on what other things you consider "logical").
The first law is just a proof using calculus, it's straight forward but a bit lengthy, it starts with the basic equations of motion (or energy), and shows that the resulting motion equals that of the mathematical equation of an ellipse.
It's a bit lengthy to repeat here but here is a small pdf: https://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf
The second law (it's the first one Kepler noticed from observing the bodies in the sky) is a bit more intuitive and it states that "if" the motion is a conic, the "area" swept by the motion (from a line at the central body) at each point and delta time is equal.
This means that the velocity at the apoasplis "must" be smaller than the velocity at the center, Oscar lanzi explained the details a bit of this law, but here is a neat animation from Wikipedia (https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion) regarding this:
The blue area stays equal in size.
So in conclusion: please be more careful on defining "is there intuitive reason" - specify why you find it "unsymmetrical", especially since you already state it is an ellipse.