Well, DD1 did the same thing and we ended up nursing one-sided.
Some of my thoughts were alignment or something else physical with her (we did take her to a chiropractor but didn't see any improvement), or different taste/nipple shape/letdown, i.e. something physical with me.
After paying close attention for a few days, I did figure out that the side she was favoring had a slower/less forceful letdown. So possibly she was avoiding the other side for a while after getting "overwhelmed" with milk from it. Another problem (I think) was that after she refused to nurse on it, the taste of the milk changed (I have read that "weaning milk" tastes saltier than it does at other times, yes I did taste it and it was indeed saltier than the other side) and she didn't like it as much as the sweeter milk she got from the other side. I guess I could have avoided that issue by pumping the one side when she was refusing it though.
Some suggestions that worked for a while (she did ultimately start refusing one side entirely, and we did fine one-sided, but I think these "tricks" kept her nursing on it longer). I tried nursing on the favored side in the football hold. She had no problem with this, which made me think it was something physical with me instead of her, since it meant lying on the same side/turning her head the same way as when she refused the other breast. Once she got used to lying on that side again she would nurse on the other breast more often (or it would sometimes work to end a one-breast strike). I also nursed her upright in a wrap. Sometimes that worked to get her to take the other breast. Both of those made NIP easier too (easier than trying to latch a screaming baby onto the breast she hates because it's so engorged it's painful, while everybody in the food court stares

).