The last paragraph of Chapter 7 of Amnon Neeman's Algebraic and Analytic Geometry book reads:

Note also that, even if the reader thinks coherent sheaves are for the birds and only vector bundles are natural objects worth studying, the proof forces one to consider coherent sheaves. The exact sequences we form in the proof inevitably will take honest, God-fearing vector bundles and make out of them Godless coherent sheaves.