I was talking to a friend who had studied history in university and he suggested that no society that had no potential for social mobility lasts for any amount of time. I suggested that ancient China was very low on social mobility; that philosophical traditions like Taoism were about the society developing ways of coping with low social mobility by valuing one's place in a larger whole. He said that all you had to do was a test to move up the ranks of bureaucracy and that that was enough social mobility to prove his point. It seems like begging the question but I don't have enough knowledge on the subject to reasonably refute his point. Please let me know if I'm wrong.
ancient China
Define ancient China. What specific periods of Chinese history are you looking at? Social mobility in China varied greatly depending on the time period, with greater social mobility during the Spring and Autumn and Warring States era.
The civil-service examination system began around 2000 years ago during the Han dynasty and was used by most of the succeeding regimes in China until 1905.
The short answer about its effect on social mobility is that it theoretically enabled great amounts of social mobility (for men only), but that in practice, of course, people who already had the resources to spend a lot of time studying for the exams were more likely to pass them.
There's a great and very readable book on the exam system, "China's Examination Hell," by Ichisada Miyazaki.
Too nuanced for a simple answer. But if I had to guess, your friend was referring to the regional test where the #1 candidate becomes a "zhuang yuan" and will be elevated to being some kind of official. I don't know if that's a practice that's considered ancient.
As far as upward mobility goes, the test was unachievable for practically all subjects within the region. The education required was far beyond what was commonly available, even for reasonably well to do families. On top of that, the test results were highly corruptible. So, using that as an example of upward mobility is like saying Ferraris are available to everyone, because we have a society that allows for being rich.