The weather cleared up after the cold front crossed the border. Why is it rainy in front and behind? Isn't this a contradiction (geography)

This problem is to distinguish the meaning of the problem. After the cold front crossed the border, it means that the severe weather changes in this area ended when the cold front crossed the border, and the weather turned fine under the control of a single cold air mass. There is more rain behind the front, indicating that the front (area) is affecting the area, and the rain area appears on the side of the cold air mass near the front. The cold front is the front pushed by the cold air mass, and the cold air mass is behind the front, so there is more rain behind the front.