Michael: "Before I was a mutineer I was a first officer in Starfleet. I'll never bear that rank or any other again. But it is who I am, and who I will always be. It is by the principles of the United Federation of Planets that I live. And by them I will most certainly die."
Lorca: "Universal law is for lackeys. Context is for kings."
Why did Michael join the crew after such disregard to her ideals? It is obvious that Lorca has his reasons - as he himself explains - for choosing Michael. The only compelling reason for Michael to join seems to be that maybe she could help fight the war she started?
Michael in the next scene: "[...] That's how I learned that the real world doesn't always adhere to logic. Sometimes down is up. Sometimes up is down. Sometimes when you're lost, you're found."
Is she saying that she's purposefully ignoring her better judgement and choosing the opposite on purpose even though it's completely illogical?
Edit: Another thought occurs. Does Michael intentionally lie in her support of the Starfleet ideals? We see in a later scene with Saruk that she has no problem lying to get what she wants even when it hurts her colleagues. Maybe Michael, who obviously knew she was being recruited, made a good speech to get out of her prison sentence? Of course it would have been a wild swing and miss since Lorca turned out to be the opposite - only Michael didn't know that yet.