I think this is very personal and you shouldn't assume this for everyone. I personally find general -> specific MUCH better, in fact this is how I learn mathematics. I first learn group in abstract, then I study dihedral group, symmetry groups etc... If done the other way around I'm always confused as to what are rules of the game.

Same. I generally prefer to see the forest first, then understand how all the different trees fit into it. Similarly when looking at a map, I very quickly want to zoom out and see where in the bigger scheme of things is the small thing I’m looking at situated.

Same with more complex concepts in math or CS - it helps me understand and retain them better if I know where they fit into a bigger scheme. Category theory is particularly interesting in this regard, as it serves to connect different branches of math into a mesh of Categories and Functors describing their interrelationships.

Learning group in the abstract, followed quickly by many examples of groups, is in my own opinion the best way to learn about groups. But this isn't quite general -> specific, this is general -> example, example, example.

I think this is where a lot of the Haskell explanations fall down, since they start with (definition of functor) -> example, example, example; then go into (definition of natural transformation) -> (no examples), and the problems multiply from there.