The first thing to understand about elite Romans like Gaius Iulius Caesar or his rival Gnaeus Pompeius Magnus is that they competed through politics. They fought each other for various magistracies which brought them and their families honour. Each political office offered a stepping stone to the next higher one as well as opportunities for wealth and military glory. The highest office was the consulate, two of which were elected each year. Competition for that was especially fierce and the voters tended to favour illustrious families that had many consulars during their history. So take the 1%, of them the (I'm pulling numbers out of my butt now but) 10% have a chance to actually be elected consul. This was going on since the start of the Republic.

Now let's go to the Late Republic. Competition is now even fiercer than ever and the stakes have gotten higher. Rome now has an empire and those provinces offer tremendous opportunity for wealth (through bribery, extortion, or even outright theft). And you need that wealth because getting elected is a very expensive process, you need to offer expensive games or races to curry favour with the electorate. Or outright bribe them. And while most Roman elites were filthy rich, much of their wealth is tied up in non-liquid assets (i.e. land). So to raise cash to bribe or woo voters you'll probably need to take out a loan and to pay off that loan you need to win so you get sent as a governor to a province where you can extort enough to pay off your creditors (and give yourself some profit). Lose and you may be consigned to political oblivion. Lastly political violence has become a thing, it's now a tool that can be used and if you have the right friends or belong to the right faction, you can get away with it.

This sets up the downfall of the Republic, competition between elites had become unstable and great men (i.e. Caesar or Pompeius) were unwilling to lose honour and would destabilize the Republic if necessary. If not Caesar, another ambitious Roman elite a couple of years later probably would've toppled the Republic (and probably not as swiftly and impressively as ol' Julius).

So the dust settles, he's now top dog in Rome. Nobody has the same level of prestige and personal standing. After he defeats Pompeius at Pharsalus in 48 BCE and to 44 BCE when he gets ganked, he's elected one of the two consuls every year except for 47 BCE. The other consul is someone who is from his personal faction.

So Caesar is usually taking one of the top offices away and the other consul is someone he chooses from his 'party'. If you're not in Caesar's faction, well you're effectively SOL and you can wave the consulate goodbye. You can watch men from non-consular families win the office (with the very weighty recommendation of Caesar behind him) while your blue blood boils. They may have been friends of Caesar, but having to curry his favour to get the go-ahead to make a run for the consulate must have been infuriating for many of the proud men who joined the conspiracy. From my perspective, it was a lot of jealousy at Caesar's success in just plain dominating the Roman political landscape and being denied the opportunity to do the same. For a few, there may have been more noble beliefs that Caesar was straight-up destroying the Republic (despite it having been left in a vegetative state since the Gracchi).