Over schemes, we can define
- locally free sheaves;
- vector bundles associated to a quasi-coherent sheaf (Stacks Project).
These notions seem to be dual to each other. It is easy to see on $\mathrm{Spec}(k)$ for a field, a locally free sheaf is a vector space $V$, and the vector bundle associated to the quasi-coherent sheaf $V$ is $V^*$.
Lemma 27.6.3 shows an anti-equivalence between the category of vector bundles and the category of quasi-coherent sheaves.
However topologically, vector bundles are defined first and its associated locally free sheaf is the sheaf of sections. This association is covariant rather than contravariant.
I wonder why algebraic geometers prefer this definition of vector bundles. Are there any conceptual or historical reasons behind this?