I recently came across a quote by Luther which reads ‘No one can become a theologian unless he becomes one without Aristotle’ [Immo theologus non fit nisi id fiat sine Aristotele] (LW 31, 12; WS 1, 226:16 (no.44)). What was the deal?
It's a rejection of scholastic theology.
From the high middle ages to the early modern period Roman Catholic Religious education was dominated by a philosophical system known anachronistically as 'scholasticism.' This name derives from 'doctores scholastici' a term used to refer to teachers of liberal arts in medieval schools and universities as well as philosophers and theologians. The term isn't coined until the mid 18th c. by which time it has already fallen out of fashion and it is mainly used pejoratively.
In a nutshell 'scholastictic' theology championed dialectal reasoning as the way to discover 'truth' and the way to defend Church Dogma. Plato's accounts of the Socratic dialogues are probably the most widely known examples of classical dialectal reasoning. Aristotle was understood to have been a pupil of Plato's who furthered developed his methodology and applied it more widely. Scholasticism developed over many centuries, shaped by figures such as St. Augustine, Ockham, Anselm et al. and had several different guises, but at basis it was a method for teaching people how they should think and by extension how the should employ rhetoric to defend their positions.
The central tenant is that 'truth' can be discovered through rational dialogue (either internally or with another person), that the human mind is capable of discerning all facts about the natural world, metaphysics, the nature of the universe ... anything... through thought alone. The infamous 'how many angels can fit on the head of a pin' question is used as a parody of scholasticism, to illustrate that the scholastics would debate anything regardless of the probability of their being able to reach any sensible conclusions.
The methodology of scholasticism wasn't just confined to Religious thought, it shaped the mediaeval world view holistically and Luther was by no means alone in rejecting it. Around the same time philosophers such as Erasmus, Descartes, Bacon et al. were doing the same. The beginnings of Humanism, Empiricism and many branches of early modern and modern philosophy from theology to the hard sciences - was influenced by the quest for alternative means of understanding. From this stems Renaissance Humanism, the Reformation, the Scientific Revolution - all those things that make our modern world view so different from the medieval world view. It wasn't a wholesale rejection of classical thought by any means, it also incorporated efforts to recover, re-translate and re-contextualise classical texts in order to reclaim their worthwhile aspects.
Luther's main reasons for rejecting the Church's scholastic theology were that it seeks to reconcile Christian theology with Classical philosophy and that it prioritises reasoning over faith.
Luther rejected the idea that the Christian Bible needed to be interpreted in the light of pre-Christian pagan philosophers, the notion that the Gospels were answerable to Aristotle was an anathema to him.
Whilst he himself was educated within the contexts of scholasticism and employed its methods for his own uses, he rejected the idea that one could discover or understand truths about God and theology through reasoning. He argued instead that a Christian should come to know the existence of God through faith and that reasoning should only be utilised as a theological tool once that basic truth was ingrained.
On the other side of the scale a generation later Francis Bacon would also reject scholasticism, but whereas Luther sought to prioritise faith as the source of truth Bacon argued for observation and so his work prefigured the modern scientific method.
Luther's rejection of 'Aristotle' used metonymously for Scholasisticm, wasn't some unusual quirk, it was part and parcel of the Zeitgeist in which he was living, thinking and writing.
I think that you should post this question to /r/askphilosophy ...