The real problem of the matter is that Manuel expected to have/obtain treatment very similar to that which Alexios I had with the participants of the first crusade, i.e. an oath of submission ( albeit informal ) which recognizes his superior authority towards Conrad and Louis ( which is a bit difficult to make a King and an aspiring Emperor accept, compared to the "simple" nobles ) certainly the small skirmishes between the Crusaders and the Byzantines during the journey to Constantinople did not help, but it goes Having said that any " feudal Kings " of the time would have extreme difficulty in constantly keeping his soldiers in line compared to the Byzantine army, therefore it is not that all the clashes were actively sought, but rather they arose spontaneously, finally there is consider the small problem of the issue, called the problem of the two Emperors, where it was very common for the two Caesars to " diplomatically insult " each other by denigrating the other as King of the Greeks/Germans, rather than with the official title of Roman Emperor ( only when relations were good or Byzantium was in a weak situation, that HRE was officially recognized as a legitimate Emperor, most of the time of the Franks, in particular cases such as Caesar of the West, prime example Otto III with Basil II ) if Manuel had decided to take the first step ( 1 ), recognizing Conrad's claim to the imperial title ( without specifying whether he was a Caesar of the Romans or not ) then it is likely that relations between the two would have immediately improved ( just see what happens then in Otl , when they became very good friends ) so the chances of the latter helping him slightly in Anatolia against the Seljuks would be good
1 ) of course we must also keep in mind that it was the first time for Manuel in which he met or interacted directly with prominent exponents of Latin Europe, therefore he had not yet developed his diplomatic ability and wide knowledge of Latin politics ( for example just see how he actually wisely tried to seek the support of the Pope and the Italian cities/nobility to take the title of HRE away from Frederick I a decade later ) , which he then naturally had in the future, therefore it can be said that perhaps out of fear of not appearing weak or politically inexperienced / immature, you insist more on his role as legitimate Basileus of the Rhomanoi, unnecessarily creating friction