Added a tag since I think some people in commutative algebra might have some comments on this.
Why are injective modules more complicated than projective modules?
For beginners in homological algebra, it is a fact of life that injective modules seems to be more mysterious than projective modules. For example, for finitely generated modules over a noetherian ring, projective resolution can be taken as resolution by free modules of finite rank, but I don't see how one can easily write down injective resolutions.
I'm wondering if there is a deep reason behind this. What makes injective modules so complicated?