Why were Greek philosophy and sciences taken up by medieval Muslim civilizations, but not contemporary Western Europe?

The answer is primarily based upon imperial geography and its particular connection with the Medieval Greco-Byzantine Empire.

The various Islamic Caliphates, beginning with the Ummayyads in Damascus, Syria, conquered much of the Middle East, the entirety of North Africa, as well as the majority of the Iberian peninsula-(though the Cordoba and Granada Caliphates would eventually establish their own independent Caliphates during the Middle Ages).It is important to mention Medieval Islamic Syria, because of their conquests of Greco-Roman colonies within North Africa, as well as the Middle East.

It remains unclear as to who "lit the spark" and subsequently destroyed the vast majority of the University and Library at Alexandria, Egypt. The Christians have been the historic villain, though there is the possibility that the Muslims may have been the ones who "lit the spark"; it still remains a mystery.

What isn't mysterious though, was the fact that Egypt, like other early Byzantine colonial lands, had major Christian institutions which helped to meticulously preserve the manuscripts from Greco-Roman Antiquity-(most notably, Saint Catherine's Monastery which is located in the Sinai and is supposedly situated next to, "THE Burning Bush"). In Alexandria, Egypt, there is the one of the oldest Eastern Orthodox Patriarchates which exists to this day. Other historic and existing Eastern Orthodox Patriarchates were (and are still), located in Antioch, Jerusalem and of course, Constantinople. Each of these cities-(with the exception of Constantinople), came under Arab Muslim occupation during the Middle Ages. Although the Muslims occupied these particular cities, there were still cultural exchanges between the rising Muslim intellectual communities of the Middle East and the various Greek Christian Patriarchs and Monks-(at Saint Catherine's in the Sinai). The city of Cairo, for example, became a major Medieval Muslim cultural and intellectual center, following the legacy of Alexandria, as well as centuries before the founding of Universities and Libraries in Late Medieval Europe.

The Muslims during the Middle Ages, also had easier access to the famed Silk Route and could quite literally carry with them, loads of precious manuscripts to Baghdad or to Bukhara in Uzbekistan. In other words, Muslim commerce-(whether land or sea based) and the transporting of precious historic manuscripts were essentially, an inseparable reality.

With regard to the cultural blossoming of Islamic Spain, Fes, Morocco, as well as Timbuktu, Mali, the transportation of Greek texts may have traveled via the various North African trade routes dating to the Roman and even the earlier Phoenician imperial age. The sea route is also a possibility with the establishment of major Muslim commercial cities along the Mediterranean coast, such as Tunis, Algiers, Tangier and Palermo-(Yes, Palermo, was conquered by the Arabs during the Early Middle Ages).

It was, however, a different story for Europe during much of the Middle Ages. Remember, the cultural blossoming of Medieval Islamic civilization, was in direct contrast to the European "Dark Ages"-(476 AD/CE-1050 AD/CE). The access to Greek texts within Early Medieval Europe was very limited-(geographically speaking). Except for The Vatican in Rome, as well as Charlemagne's Aachen in Northwest Germany-(circa late 700's AD/CE), as well as the nearby cities of Trier and Cologne, much of continental Europe 1000-1500 years ago, was culturally stagnant and primitive. Illiteracy and religious superstition were widespread, a lack of scientific and medical sophistication were commonplace and the translation of Ancient Greek works were almost exclusively conducted by Monks and Scribes employed by The Vatican. This of course would change with the following events: the Spanish Reconquest beginning in Northwest Spain, the Crusades and (on a less warlike note), cultural exchanges between The Catholic Church and Muslim communities in Toledo and Cordoba, Spain, at the beginning of the 2nd Millennium AD/CE.

Keep in mind, that cities, such as London and Paris, were just mere towns during the Early Medieval period-(when compared with the above mentioned German cities, Rome, the cities of the East, as well as much of Spain). The concentration of power, as well as financial and cultural wealth had shifted away from Rome with the relocation of Roman imperial power to Constantinople by Emperor Constantine-(and to a lesser extent by his predecessor, Diocletian). The redirection of power, wealth and culture would eventually contribute to the decline and deterioration of Rome, but more specifically, to the majority of lands and peoples living to the NORTH of Rome-(with FEW exceptions).

Overall, the survival of Ancient Greek texts is primarily due to the Greeks themselves who created their own legacy of academic scholarship and preservation. However, it was the Muslims, who also preserved the Ancient Greek legacy, but unlike the Greco-Byzantines, furthered the Ancient Greek legacy with great creativity and originality. So before one turns to the Chapter on Late Medieval Europe and "The Age of Scholasticism", please make sure to study the earlier chapters on Byzantium and in particular.......the Medieval Muslim Age.

Greek knowledge was mostly written in Greek, which was only known in medieval times on the easter side of the former Roman Empire. Arabs took this knowledge after they conquerer these lands (Egypt, Palestine, Siria, etc) and moved it to the west to Spain.

There, in Spain, several erudites like Ibn Rushd (Averroes) wrote important works based on Greek knowledge. And were the works of these arabs the ones that entered to the west in the late middle ages.

Finally, after the fall of the Roman Empire in the west, few people actually was literate, most of them monks (who were able to read Latin, not Greek). That's why most Greek scripts were lost there.

I'm not sure how accurate it is to say that medieval Europe did not adopt Greek philosophy. Mainly because Ibn Rushd, whom you mention, inspired Thomas Aquinas. Both men reconciled their religious traditions with Greek philosophy, and Thomas was born just a century later than Ibn Rushd. It's worth noting that the Catholic church was the only real centre of learning in Europe, and as such it did promote knowledge gained from the Romans, and after Thomas, Greek philosophy too. But with illiteracy much higher in Europe, and books being very expensive, that wouldn't have translated into popular knowledge.

Easy in the east

Greek culture was known and respected by muslim rulers because they conquered the lands in which it was popular and accessible. Furthermore they were centuries of conflict between the Byzantine Empire and what is nowadays Iran and several muslim adversaries that led to numerous advances and retreats. Thus leaving behind a population of people immersed in both cultures.

To give a sense of the scale of the wars between Iranian powers and the Romans, you have to know that both parties moved entire towns trying to hold on the land that they temporarily occupied. This started before the fall of the Western Roman Empire.

Since Spain was part of the muslim-held areas they were frequent encounters with other muslims countries, at least among the ruling class, and more importantly trade which helped mutual understanding and create a pathway to maintain cultural relations.

Difficult in the west

On the other hand in the Europe there has been the collapse of the Roman civilization, which made very difficult to mantain a class of people knowledgeable about a foreign culture.
The Romans had spread their language and culture on the western part of the empire, which was culturally poorer at the time of their conquest, but they had maintained ther richer hellenic culture on the east. In short, there was a void that couldn't be maintained.
Another obstacle was that the west was generally poorer for a long time, the first rich cities of the west were probably the Italian city states.

You could also add the quite open hostility between the Pope and the Orthodox Church and even the Empire of the Greeks and the Empire of the Franks. And, occasionally, there was an open war.

You shouldn't also forget that to travel and to create books, translating them and make them available to a large number of people, even among the elite, was very hard at the time.

[1] Probably also influenced by the long problems of Arianism