We have a 2,5 year old daughter. When I attempt to do something for her (be it warming her milk, changing her clothes or picking her up from the highchairs), most of the time she says "Don't do it. I want mommy to do it". When we asked why, she first refused to tell us, then she told us "I'm afraid of lions". A little background here: We would tell her "Daddy is strong as a lion and he will always protect us", I would roar and we would all have a laugh. When she said she was afraid, we agreed I would never be lion again, just strong, and she nodded. These days, the same behaviour started occuring. When my wife asked her, she would say "I don't know". How do we get her to tell us the (real) reason?
Children tend to go through phases where they strongly favor one parent, which seems to be happening to your daughter. Your daughter wants to maximize time and attention from her mother, that's why she protests if you do things with her that her mother would otherwise do. You're not doing anything wrong or different, you're just not mommy.
This phase will pass again and who knows, in a few months mommy will not be allowed to do anything with her. In the meantime, you're stuck with the protests every time you try to help or interact with her. Stay calm, be persistent. If she learns that protests and screaming get her mommy's attention, it'll get worse.
One thing that may help is for the mother (favored parent) to be out of sight or "away" in some form that your daughter understands she's not available. "Mommy is busy" doesn't count for that, but "Mommy's taking a shower" or "Mommy's out doing the grocery shopping" may.
Above all, don't take it personally. There's absolutely nothing you did or can do about such a phase, it's just part of a child's development.
Is it possible something could have made her afraid of men? One time, long ago, a woman told me that her daughter was afraid of men as she explained why her daughter would hide behind her mom's leg and peak around at men in a very shy manner.
I'm just throwing that out there as a possibility because of what I know somebody else experienced. It may not be that at all.