The first time you talk to Miranda on the Citadel, she mentions she's been "hiding from just about everyone" and that she is no longer involved in Cerberus. I don't remember this happening at the end of ME 2. Why did she leave and when was it revealed?
If you take Miranda with you into the final fight on the Suicide Mission in ME2, when Shepard goes to rig the base to explode, the Illusive Man opens a channel to convince Shepard to "not do anything rash".
When this fails, (again, assuming Miranda is in the party), he entreats Miranda instead to "stop him".
Miranda refuses, and the Illusive Man warns her that she's endangering her position within Cerberus. She responds, "Then consider this my resignation".
The events of ME2 has planted the seeds of doubt in Miranda about Cerberus.
There was the event of the 'disabled reaper ship', where afterwards the Illusive man admitted that he manipulated them in despite knowing it was a trap which probably started the distrust.
By the end of the game, even if you took the renegade option at the end of ME2, and you talk with Miranda afterwards, she will express that she's not sure if handing the collector base over to the Illusive man was a good idea.
I think the endless manipulation of the Illusive man has shown her that he's not to be trusted which led to her eventual resignation.
If you actually romanced her in ME2 and have the Shadowbroker DLC, Liara will also comment about how much she has changed since their first meeting in Illum (when she was very focused to Cerberus).
Honestly I think Miranda just started seeing the Illusive Man as someone who doesn't care about who lives or who dies. As long as he gets what he REALLY wants - he's satisfied.
When planning to destroy the Collector Base, Miranda DID care about what happened to the colonists that were abducted by the collectors. Did the Illusive Man care? No. All he cared about was the power of Reaper tech.
Miranda saw Shepard as a better protector of humanity than the Illusive Man himself. After learning the Illusive Man wants the Collector Base's power, Miranda chose her Commander over her boss because not only did she believe in Shepard, but she started accepting Shepard as a friend after they helped her with her sister.