Probably the necessity of space travel. Interplanetary, and interstellar, transportation would present a huge threat - crashing an FTL ship at a target would be a comparatively cheap and effective way to devastate large populations. I would expect the military to heavily police and regulate this - we don't see many privately-owned spacecraft in the Haloverse, or at least no large freight or passenger craft. We know that the flow of traffic must be significant, with inter-colonial trade being a major industry. Proportionally, then, the military must be large enough to staff and maintain these ships. These ships would also be targets for piracy, so they must be large enough to protect these trade routes. So we see, even in the pre-Insurrection era the potential for military control is significant. The CMA and the UNSC were distinct entities, so I imagine the CMA mostly ran the Outer Colonies semi-distinctly from Earth control, but with Earth oversight - without having a toe in the water, so to speak, the CAA would have little clue about how its policies would really affect the colonists. So we see the potential for resentment directed at Earth and the relatively closer Inner Colonies, who benefit from better infrastructure and familiarity to the CAA. And then, as the Insurrection spreads through the colonies and the CMA proves utterly inadequate, the UNSC has to expand and consume its former sister-branch to cope. By at least the end of the Human-Covenant War, humanity has lost so many colonies and so much infrastructure that the military is forced to take control of things to stop it falling apart.
Frankly, I think the use of the UNSC as the outward face of the government is a gesture of honesty on their part. We all know that humanity is under a military dictatorship during the Great War, even if it is a relatively benevolent one under Hood. We see in places in Asia and Africa, and formerly in Eastern Europe, that military governments try to present the face of a civilian government to cement their legitimacy, but that doesn't stop resentment. It just paints the military as a target, and promises a true democracy if it is overthrown. Why present its populace with the illusion of democracy? By refusing to present the illusion, Hood doesn't look to be consolidating his own power. And we see in Glasslands, whatever we think of the novel or the writer, that Hood is actually transitioning power back to the civilian government. So I think that while the Insurrectionists were justified in their concern over military control, that in practice they vastly overreacted, forcing the UNSC to react to them.
It reminds me of foreign attitudes to America, in a way. You never see protests in the streets condemning the US Military for whatever scandal has them up in arms - they blame the entire nation, and its entire population, because they refuse to differentiate between the actions of a few and the intentions of a nation. The Libya incident, for example, was set off by one idiot director's bad dub of an originally harmless movie. Because the US refused to force Youtube to remove it, they decided that it was yet another American conspiracy against them. They simply did not see the difference, because in their own way of life there is no difference. I can see cultural filters playing a part in the colonies' perceptions of Earth and the UNSC - they would have to deal with UNSC ships, personnel, officials and regulations a lot more than those of the UEG, so the UNSC would become the public face of Earth-controlled government.
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