The Illusive Man was indoctrinated. I'd imagine the Reapers altered his thought patterns so he thought capturing the citadel would help his goals. It could be seen as a way for the reapers to control the citadel without a frontal assault (they obviously need the Citadel's help in harvesting the human race, they could control the relay network and the reapers knew about the crucible plans).
Pretty much this. It makes perfect sense when interpreted that way (and really, only that way).
Javik tells you that in his cycle, an Indoctrinated splinter group - analogous to Cerberus - tries to control the Reapers, fragmenting the resistance and causing the Crucible project to fail. In this cycle, TIM was exposed to Reaper tech early on, and if that wasn't enough he keeps the remains of a dead Reaper core literally outside his god damned office door, then he implants Reaper tech into every one of his soldiers and deliberately indoctrinate them.
The Reapers used Cerberus to oppose the Alliance. Every time allied forces are stuck fighting Cerberus, they aren't fighting the Reapers. Basic divide and conquer and diversion strategy. Meanwhile, TIM is deluded into thinking he is fighting for the good of humanity - ironically enough.
The Reapers use Cerberus to try to take control of the Citadel without losing any Reapers or Reaperized troops. Simple enough strategy. As a side note, Javik also mentions to you that the Reapers in his cycle allowed people to gather at refugee camps, in order to sneak indoctrinated refugees in and take them down from the inside. Although the Coup was bit different, it seems like they've used similar strategies before.
People often raise Sanctuary as an objection to the idea that Cerberus was always indoctrinated. But according to Javik, it is highly suggested that the Reapers actually implanted the idea that they could be controlled in the minds of the indoctrinated splinter group, perhaps suggesting that they did so with Cerberus as well. That would be an interesting possibility, and would require further consideration as to why the Reapers really attacked the place. However, a simpler explanation is that like Saren before him, who created a research base to study indoctrination while he was himself indoctrinated - so too did TIM create sanctuary. Although indoctrinated, he still had some degree of free will, just like Saren. If he didn't, he would be useless as a puppet.
The writers also weren't even particularly subtle about it. It is obvious that they wanted you to make the connection that Cerberus was indoctrinated from the start. Early in the game and proceeding throughout it, multiple major characters (such as Anderson) ruminate on Cerberus being indoctrinated and "working with the Reapers". Some even state with with matter-of-factness as if everyone already knows it to be true. And when Shep gets to Sanctuary, he is openly perplexed and says "I thought Cerberus was working with the Reapers?". They literally bash you over the head with their indoctrination.