It seems the approach to learning category theory depends heavily on taste.
I just wanted to say something to contrast "that's a guaranteed way to learn to hate it":
I learned category theory from reading Mac Lane linearly (but over a long time, and later I put in some abelian categories from various other sources). First, because I needed to know what a functor and a transformation are. Then I discovered how good it is at unifying stuff and tried to make up examples as I read along.
I enjoyed this "abstract" approach to category theory, but I don't want to "do" category theory. I guess you just have to learn a few abstract concepts, see if this kind of learning pleases you and then decide which way to choose (the good references for the different ways are given here).
To give an example, you could try to understand what a limit, in the sense of category theory, is.