Not Europe.....The Seljuk Turks (not Arabs) and the Byzantines were vying for control of Anatolia, which was part of the Byzantine Empire and parts of it (Syria) had been taken from the Sassanids, Fatimids and then the Great Seljuq Empire in the first place......Also during the 11th Century the Reconquista in Iberia (Berbers, not Arabs) was already taking place and The Normans were just as concerned with conquering the Byzantines as they were the Seljuq's.
The Muslim Conquests in Europe were hundreds of years prior to the First Crusade and were mainly limited to southern Iberia and a very short lived incursion into southern Italy. The majority of Muslim Expansion was in Arab, Middle Eastern and Asian lands rather than Europe. The Byzantine-Arab wars had been going on for hundreds of years, with each vying for Asia Minor rather than Europe. It was the Byzantibpnes that were guilty of pushing into Europe and the Euopeans (Normans) guilty of numerous incursions and expansions into the Byzantine Empire. The whole geo-political nature of the entire region was far to complex to simply point to one group (or religion) and say 'they started it'......the fact is the the people's of the Middle East had been subject to one foreign Empire or another since Alexander (if not before) and the spread of Islam was predicated by that particularly in the traditional indigenous ethnicities of Asia Minor.
You are right that it is not relevant to modern issues in the Middle East and Asia though. That is a whole different ball game, one which the West has had a hand in as well, notably with the carve up of the Ottoman Empire and the end of the Caliphate.