Category theory is a must if you are into some fields like algebraic geometry, number theory, topology, etc. In those fields, people use it more than set theory.
The power of category theory comes from its relativism, generality, intertwining many fields into one. Unlike set theory, you can map topological spaces to groups, their homeomorphisms to homomorphisms in category theory. Of course you can do like that with any other mathematical objects. And you can build a category theory without objects (in fact, the identity morphisms are sufficient to replace all the objects) so you can get all the property of objects not from the objects themselves but only from their relations. Thus you can get result by only drawing some diagrams. This is called "Abstract nonsense" (https://en.wikipedia.org/wiki/Abstract_nonsense