Quoting Wikipedia:
The subsequent development of category theory was powered first by the computational needs of homological algebra, and later by the axiomatic needs of algebraic geometry, the field most resistant to being grounded in either axiomatic set theory or the Russell-Whitehead view of united foundations.
It is clear now that Algebraic Geometry has benefitted a lot from the language provided by Category Theory, but, historically, what were the complications when people tried to formulate A.G. over the language of set theory?
Why did we require Category Theory?