What makes farming in mountainous areas so difficult without terracing?

The steeper the land, the greater the tendency for dirt to wash down hill when it rains. If the land is absolutely flat, rain water has nowhere to go but down into the soil. If the land is slightly tilted, any water that cannot be absorbed immediately will start flowing downhill. If enough water runs downhill it can wash out a gully. The steeper the land, the easier it is to get gullies started. So the mountainous areas are usually the ones that have the steepest slopes. On top of that, rocky soil does not absorb water very well.

When plowing, if the furrows go downhill, that will make water run rapidly downhill. If the furrows go across the hill so that the elevation of each furrow stays constant, then rain will go to the bottom of each furrow and not be led straight downhill. When slopes are moderate, people use contour plowing and you will see curvy furrows the tops and the bottoms of which are level.

In the mountains, contour plowing is not enough. If you used only contour plowing, the water would go over or through the furrow walls and soon wash out a gully. Soil erosion would ruin the farm. So in places with steep slopes you have to build walls along a line of equal elevation (so the top of the wall is exactly level), and then fill in the soil behind the wall so that it is all level. Then the only other things you have to do is make a way for water to leave the terrace (if it gets too deep) without going over the top of the terrace wall and washing it away.