Moonrise location


First I would like say that I’m completely uncultivated in astronomy.

I know moon appears to rise east and moves west even tho it rotates in the same direction as earth.

The question I have is about north/south. Last month I was observing the moon every day and I could see it doing a slow south-east to north-east transition on rise. Every day it appeared a bit more to the north. Then new moon came, and two or three days later it was at full south again.

I’m confused cause the transition to north seemed to be slow and it went back to south really fast.

Any one could explain to me?

Thanks a lot