I have a basic knowledge of this period so I'll help where I can.

Note: this is largely from memory, based on my third year of university, which I left in 2011. If I miss any glaring details, or simply get something wrong, I apologise in advance. I'm hoping someone better qualified can come in and fill in the gaps and set the breaks I'm about to write.

From what I understand, there was never really a concord between Byzantium and the Crusaders. Remember that the Byzantines saw themselves as the inheritors of the power of Rome, whereas the Crusader's power was imbued from the Pope in Rome.

In AD 1054 there was a schism between the eastern and western churches when envoys from the Pope marched into Constantinople and basically threw the gauntlet down against their orthodox cousins. That rift never really healed (it still hasn't).

When the warriors of the First Crusade arrived outside the walls of Constantinople, they arrived in a horde. To the proud Byzantines, they appeared as a conquering army from the Patriarch of Constantinople's rival, the Pope. As a result the Byzantines did not allow the Crusaders inside their city, instead selling food and supplies to them at (reportedly) exorbitant prizes, lowering it down from the mighty walls of the city. Considering that the Crusaders thought they were on a mission from God, they must have seen this as only further evidence that the Byzantines were heretics - not to be trusted.

When the Crusaders set off from Byzantium, they faced a large army of Seljuq Turks in Anatolia, and had no help whatsoever from Constantinople.

As the Crusaders eventually succeeded, this meant that the pontiff in Rome had a huge base of power and support in the Holy Land, territory historically owned by the powers of Constantinople. This, tied with numerous smear campaigns from both sides, only increased the tensions.

That's about where everything I can remember runs out. Hope I've helped at least a little bit.