Muslims and Christians

Based on the Christian documents, it does not seem possible for them to have had a more positive relationship with Muslims.  William of Tyre, the archbishop of Tyre, had nothing positive to say about the Muslims.  He seemed to have antagonized them at every given opportunity.  In Tyre's story of the Muslims blaming the Christians for placing a corpse of a dog in a Muslim temple, Tyre expresses his dissatisfaction against the Muslims; they threatened to slay every Christian for the action of a Muslim infidel.  This situation seems like a reasonable one to express his dissatisfaction of the Muslims.  However, in his first statements, he claims that Muhammad is not some proclaimed prophet.  Rather, he is an infidel who is the Son of Satan.  This antagonization of Muslims had no specific event to inspire it.  It was simply said, from what I know, from frustration.  And something coming from someone as high as an archbishop has the power to influence many others.