Foreign Policy magazine takes on some of the arguments against allowing highly skilled or educated people in poor nations to leave if they want to. The nub of their points:
This common idea that skilled emigration amounts to "stealing" requires a cartoonish set of assumptions about developing countries. First, it requires us to assume that developing countries possess a finite stock of skilled workers, a stock depleted by one for every departure. In fact, people respond to the incentives created by migration: Enormous numbers of skilled workers from developing countries have been induced to acquire their skills by the opportunity of high earnings abroad….
Second, believing that skilled emigration amounts to theft from the poor requires us to assume that skilled workers themselves are not poor. In Zambia, a nurse has to get by on less than $1,500 per year—measured at U.S. prices, not Zambian ones—and a doctor must make ends meet with less than $5,500 per year, again at U.S. prices. If these were your annual wages, facing U.S. price levels, you would likely consider yourself destitute. Third, believing that a person's choice to emigrate constitutes "stealing" requires problematic assumptions about that person's rights. The United Nations Universal Declaration of Human Rights states that all people have an unqualified right to leave any country. Skilled migrants are not "owned" by their home countries….
The belief that skilled emigrants must cause public losses in the amount of their training cost is based on a series of stereotypes. First, large numbers of skilled emigrants are funded by themselves or by foreign scholarships. A survey of African-born members of the American Medical Association conducted by one of the authors found that about half of them acquired their medical training outside their country of birth. Second, many skilled emigrants serve the countries they come from for long periods before departure….
Skilled migrants also tend to earn much more than unskilled migrants, and on balance this means that a university-educated migrant from a developing country sends more money home than an otherwise identical migrant with less education. The survey of African physicians mentioned above found that they typically send home much more money than it cost to train them, especially to the poorest countries….
The article also casts doubt on the notion that skilled emigrants never return to their countries, or that poor medical outcomes or care in poor African countries can be meaningfully blamed on emigrating doctors.
On the other side, the article also says we shouldn't overstate the benefits of skilled emigrants in building up trade and investment ties between their home countries and the wealthy west. Still, pragmatic arguments meant to lead to the conclusion that skilled professionals in poor countries really ought to just stay put are weak.