The Abbasids wanted to show that they could carry on Hellenic culture better than the Greek-speaking Byzantines, benighted as they were by the irrationalities of Christian theology.
And the early Christian 'establishment' was consolidating power, deeply uneasy with the remnants of Greek intellectual tradition (too closely linked to paganism). "Doubt" was not something they could afford to promote (*cough*). Until Aquinas, they never could create a framework for Aristotle et al to be integrated into religious canon. The Arabs knew a good thing when they read it.