Not an expert, but an enthusiast. The universe can typically be considered homogeneous and isotropic on a large scale (it looks the same in all areas, and also looks similar no matter which direction you happen to be looking) for the sake of understanding and performing physical calculations. The beach may also be considered homogeneous and isototropic, but we know that if we dig down, we'll find interesting materials, organisms, and even various grades of sand (for context).

The universe is roughly symmetrical even though there are structures and features of great complexity when you look close enough (such as atoms, you, me, horses, and icebergs). This is probably because the universe originated from a single infinitely dense point where there wasn't room for much diversity or clumping of matter. As the universe expanded, random quantum fluctuations and coalescence, perhaps due to gravity and the various electrical and atomic forces, is to thank for the formation of elements, stars, and galaxies, over the last 14 billion years (or however old the Universe is supposed to be).

Anyways. It's represented as symmetrical because it's convenient and true on a large scale, but its always more complicated the deeper you look.