There are certain characteristics of both left an right that are not always that obvious. But the hierarchy vs equality conflict is of thousands of ages, even if modern political parties don't reflect that.

Humanity is like a pile of random elements (individuals) that always revert back to the mean, this is where the force of equality comes from, it's a biological manifestation of this basic mathematical truth.

And the force of hierarchy is just the forces of Darwinism at play, as humans tend to group together in order to survive.

It's just a biological conflict inside us, the 2 forces that fight against eachother, regardless of what political movement they show up these days.