Maybe I'm just being naive, but the way I see it, these were men who had grown up with Alexander. They were tutored around him, raised alongside him, went to war, fought alongside him and followed Alexander to the edge of the world (by Greek standards anyway). Really, if that didn't bind them together and give them a sense of brotherhood and comradeship, then I don't know what will.
So why, mere years after Alexander's death, were they tearing each other and his empire to pieces? Were they all consumed by the same power hungry tendencies? Was it the treachery of one that turned them all against each other?
Why were they so willing to forgo all bonds of friendship and brotherhood and lose all that they had built? Certainly, not all of his generals and companions were childhood friends, but you would think that there was a certain sense of loyalty amongst them.
I'm probably being very naive and romanticising the politics and relations between the diadochi, please feel free to correct me
It's important to appreciate the magnitude of Alexander's personality and the importance of his leadership. While I don't want to stray too much into great man history, I wouldn't consider it an exaggeration to say that Alexander was holding the whole enterprise together by sheer force of will. After all the campaign's objective of retaliation against Persia had been accomplished after Guagamela and perhaps even earlier when Darius sued for peace. Nonetheless Alexander pushed on deeper and deeper into the heart of Asia, increasingly not in the interests of Hellenic retribution against the dastardly Persians, but more and more just to fill his own grandiose dreams of conquest. While his ruthless pursuit of Bessus and subsequent honoring of Darius speak to a strategic motive of linking himself with the Persian legacy, the fact that he went as far as he did indicates that he was now aiming for the end of the world (as he knew it). So when he finally died there was a gaping hole that no one could fill. He alone had willed his men to keep following him and the empire he had built was more his than it was that of the Macedonians. Furthermore, as the undisputed king he had the power to remove disobedient officials and keep his administrators in line, something he did with alarming frequency in his later years. When he died there was no clear authority figure who could keep everyone under control.
But we should not limit ourselves merely to Alexander's extraordinary leadership. For in many ways the turmoil that consumed his world after he died was the product of a lack of governmental consolidation. Alexander had spent his entire reign campaigning rather than ruling. He was constantly on the move carrying out some war against someone. While he did appoint and replace officials, organize provincial constitutions, impose taxes, establish cities, and make calculated public displays of one sort or another the day to day administration of his domains was carried out by increasingly distant subordinates. Just look to Anatolia where by the time he died the men ruling it had been doing so for nearly a decade and more-or-less autonomously. For example, Antigounus had been ruling Phrygia for ten years by 323 without much in the way of central direction. Why would he give up his autonomy to some nebulous imperial authority just because Alexander died? Alexander's brief sojourns in the territories he conquered meant that the various provinces became the personal fiefdoms of their governors. Cleomenes' extortionate regime in Egypt and Harpalus' non-stop party in Babylon are good examples of this. The Persians had enough trouble keeping their vast empire together and they had a clear and established monarchy to preside over it, one whose king wasn't wondering off into India with many expecting him never to return. Alexander was always so occupied with campaigning that there was little in the way of a clear cut system of control.
But what about the bonds of friendship and Macedonian camaraderie? Wouldn't these men who had accomplished so much together be able to stick it out in the service of unity? It's here that we have to accept that the Diadochi were extraordinarily ambitious and self-interested. These were men who would build kingdoms and found divine ruler cults. The ruthless ambition of these people shines through immediately after Alexander's death. Perdiccas, the most senior general, essentially bullied everyone else into accepting him as the regent of the empire. His original idea was to wait for Alexander's child by Roxanne to be born and see if it was male (i.e. eligible for the throne). Of course not everyone wanted this. Ptolemy was part of a faction that called for a junta of generals to rule rather than the motley selection of possible royal heirs. Perdiccas and his cronies (one of which included the illustrious Docimus) were of course very much against this but there was a third party. The common men of the infantry, led by Meleager, felt a strong sense of loyalty to Alexander's family and were prepared to put his mentally impaired half-brother Philip on the throne in the name of dynastic continuity. Meleager was probably hoping to manipulate Philip by advancing this. So what we have is a stand-off breaking out immediately after Alexander's death. This was only resolved by a slapdash compromise that saw Philip join Roxanne's baby (it turned out to be male) as a joint king under Perdiccas the regent. Meleager and his men were executed soon after and Ptolemy, whose idea had been sidelined, was sent off to Egypt.
Such a bitter dispute breaking out so quickly really sets the tone wouldn't you think? These were people who saw a chance for great personal advancement and risked a lot to get it. The theme of course continues as we find Macedonian officials acting like independent rulers within a year of Alexander's death. Ptolemy acted independently to expand his province into Libya almost as soon as he took over. Peithon was trying to build up his own power base in Bactria around the same time. Antigonus flat-out ignored Perdiccas' instructions to help a man named Eumenes take over the unconquered territory of Cappadocia. These men may have all known each other for a long time and some of them may even have been friends, but they were much more interested in their own power. Their goals may have varied, in that Perdiccas (and maybe Antigonus) arguably wanted to consolidate power over the whole empire while Ptolemy, for the most part, was interested in tightening his grip on Egypt but they were all looking out for themselves in some way.
Of course this is not to say that Alexander's name didn't command respect or that the concept of a unified empire was done away with immediately. As late as 311 the Diadochi were maintaining the pious fiction that they were ruling in the name of the royal family. Ptolemy's redirection of Alexander's funeral possession to Egypt was a calculated ploy to cultivate prestige, as was Perdiccas' intention to marry Alexander's sister. Entire armies changed sides because the enemy had a closer affiliation with Alexander's family. So there was certainly loyalty and mystique associated with Alexander this was something the Diadochi used to further their own ends rather than acting together to try and make an attempt at unity.