Who doesn't want equal rights?
Gender equality, racial equality, you name it.
However, there seems to be a general disagreement on what “equality” should look like.
I'd like to present my viewpoint using the mathematical definition of an equivalence relation, which is basically a generalized idea of equality.

Reflexivity

Reflexivity simply means that everything is equal to itself.
This is not really relevant when discussing human rights, since the rights of a given group are equal to themselves by nature.

Symmetry

Symmetry says that if X is equal to Y, then Y is also equal to X.
In other words, two equal things are interchangeable.
Now this gets more interesting.
My interpretation is that if switching the roles of two people/groups wouldn't change their situation regarding what they can do, only then can we say that they have equal rights.
Surprisingly, this already seems to be a very controversial opinion.
I'll get to concrete examples later.

Transitivity

Transitivity says that if X is equal to Y and Y is equal to Z, then also X is equal to Z.
It's hard to imagine a scenario where this would come relevant in human rights.
After all, it involves three variables, but discussions about human rights usually compare the rights of two groups.
We'll see if this becomes useful later.