Big city means big population?

Jody Seaborn made an opinion writing to comment on the article  of Juan Castillo about the new ranks of big cities in the U.S.
Austin is ranked 11th at the moment. Jody pointed out that Austin's population has been increased steadily for years. However, he made his idea that population cannot tell about the size of the cities. Moreover, he leaded to the point that even how fast Austin has been growing, it still cannot beat the other cities within 10 years. I agree with this idea. At the time Austin is increasing, we cannot tell that others are increasing the same way or not, it depends on the immigration and moving in and out of residents. With his explanations on San Francisco and Austin, I think it is true. Austin and San Francisco are both on the list of important cities in the U.S, which attract people to move in for jobs. So there is no proof to show that when Austin gets the bigger population, the others do the same or opposite way.
Big city does not only count on the population, it needs to count on more than one aspect, such as population, annual income, living condition, rate of employed and unemployed, immigrations, available jobs, and so on. Even though Austin is getting higher in population,  but at other aspects, it is still lack of, we cannot call it at a big city. However, we can give a future on it not so far from today.