1.She never ask a spectre to transfer her, she ask her sergeant, you are just eavesdropping.
2.Knowing her brother was a part of Cerberus may cause her to hesitate in combat causing not only her death but the death of other marines and the failure of their mission. It's not as selfish a request as you think.
3.Most grunts don't know about indoctrination.
4.Their is no reason for her transfer to result in problems as the alliance should just swap her out with another engineer who doesn't have a problem with fighting Cerberus. I'm sure many would rather fight the human terrorist rather then the reaper abominations. That result was rather poorly thought out.
This. Military officers are often rotated out if their superiors believe there's a conflict of interest - it's why married officers are generally kept out of the same chain of command. Especially in a case like this, where the enemy is literally her brother, her hesitation on any battlefield with Cerberus soldiers could get people killed. It's selfish, sure, but it's also acknowledging that she is in a position where she is likely to be a liability to those people who rely on her, which is her taking steps to watch out for them.
If anything, I wanted to be able to tell her that her brother is likely dead, rather than simply have the choice of approving or denying a transfer request. If Shepard can overhear these conversations, why can't they say anything?