Why is the ridge of high pressure warm and sunny, and the trough of low pressure cool and rainy?

Downflow prevails in the high-pressure control area, so the weather is fine. The low pressure control area is updraft, and water vapor is easy to condense into clouds, causing rainfall.

It is impossible to form a front on the ridge of high pressure because the high pressure diverges in the horizontal direction of high pressure, and there will be no cold and warm airflow meeting, so it is impossible to form a front.

The low pressure diverges and converges in the horizontal direction, so there will be a situation where cold and warm airflow meet to form a front.