What is the root cause of the invincible conquest of the South and the failure of the Northern Expedition in the Han Dynasty?

Personally, I think that the southern expedition of the Han Dynasty was invincible and the northern expedition was unsuccessful. The fundamental reason is that northerners think that southerners are not strong in fighting capacity, thus underestimating southerners.

The direct consequence of the continuous migration of population to the south is that the garrison on the northern border cannot obtain food and manpower locally, and the food can still be solved by reclaiming land, but the manpower supplement can only be transported from the distant hinterland of the Central Plains, which has caused an extremely heavy burden. At that time, in order to completely solve this problem, many dynasties adopted tough measures to relocate residents, which was a kind of "real border" and tried to send some criminals to the army. However, because this goes against human nature, as long as the management is relaxed a little, or in case of war, these residents will immediately run away and go south.

It's already so difficult to simply guard the border, not to mention the Northern Expedition. Although the ruling class has sufficient reasons for the Northern Expedition based on political and military factors, ordinary people accustomed to the comfortable environment in the south are the main force of the army. They don't want to fight and they don't want to fight. How can they win?

However, when the dynasty conquered the south, it was often immigrants who reclaimed wasteland and formed villages. What the government army did was to help them repel the counterattack of the local aborigines, so the immigrants naturally reciprocated and distributed food to the people so that the army could concentrate on fighting. However, after the aborigines were subdued and assimilated, only a small number of troops were needed to maintain stability, so it was also the credit of immigrants. In the Southern Song Dynasty, the Ming Dynasty and the Qing Dynasty, the actual line of control continued to push south and southwest, all for the same reason.