Meritocracy Lacks Intrinsic Incentives To Benefit Others
One of the objections to meritocracy is that in the absence of a deep cultural commitment to reciprocity (such as the Confucianist philosophy that went hand it hand with the meritocratic civil service exam system of the Qin and Han Dynasties of China) or a representative democracy, that the elites in positions of power will abuse that power for their own ends rather than respecting the legitimate needs and desires of those who lack merit and are not in power.
Politics involves both power and choice. A meritocracy, pretty much by definition, grants power to people who are most capable of evaluating and implementing the best available choices. But, the ability to evaluate choices well doesn't mean that the meritocratic elite will make choices for the good of the many as opposed to their own personal self-interests as a class, unless there is some cultural or political mechanism in place to cause them to serve the people selflessly. When a meritocratic class looks out only for itself, you end up with a social Darwinist system that many people find to be morally abhorrent. Often meritorious elites have different political interests than other members of a society.
In this regard, criticism a meritocracy are similar to criticisms of nominally meritocratic efforts to limit the franchise in representative democracies, for example, by limiting it to property owners or imposing literacy tests or excluding felons from voting. Because, while these reforms may indeed reduce the share of voters who are ill informed about issues of public policy that are indirectly resolved in elections, potentially resulting in bad choices by voters as a whole based upon the decisions of the ill informed voters, a limited franchise also creates a political system that can systemically ignore the needs of people who are denied the right to vote without political consequences for doing so, thereby harming the people who are denied the right to vote.
Ancient China (discussed in the links above) tried to address this inherent flaw in merit systems by making good moral character in the sense of the Confucian notion that a superior has a binding moral obligation to look out for the well being of his inferiors, an element of merit (defined in modern parlance in terms of cognitive and executive ability and work ethic), rather than as something distinct from it.
Modern representative democracies seek to address this inherent flaw by creating institutional incentives in the electoral system for elected representatives to act in a way that makes them popular and discourages powerful or numerous factions from organizing against them, even though when implemented, these incentives don't always work as intended in the raw political theory. And, the political theory of representative democracy can overestimate the ability of voters who may lack merit to choose representative who have merit and will faithfully carry out the will of the voters.
This is less of a concern in a well regulated mixed economy, where government regulation and market incentives discourage elites in independent business firms from acting contrary to the needs of members of the society because profits can be earned only by entering into transactions deemed by the parties by mutual consent to be mutually beneficial since regulation punishes firms that engage in deceptive conduct or creates externalities that impose costs or harms on someone without their consent.
Abuses by meritocrats in the private sector are also discouraged by the cultural value of pride of ownership by which an owner of property derives personal satisfaction from having property whose quality is recognized in society as having high quality. The sense of having a stake in a community and something to lose if the community fails to function promote pro-social conduct by meritocrats in the private sector.
This pride of ownership cultural cue may have less of a powerful effect in government and publicly held companies, however, where a fundamental concept (outside of monarchies and feudal systems) is that the elites who run these institutions do not own them and instead merely manage them on behalf of others, which can give rise to what is known as the principal-agent problem.
But, corrupt self-interest is a serious concern in the decision making leadership of sovereign governments because, by definition, they regulate others without being subject to regulation that effectively prohibits self-interested action themselves without some sort of cultural or institutional check on abuses of this kind. (This is sometimes called a "who watches the watchmen?" problem which as been widely discussed since classical Greco-Roman times.)
This can even undermine the meritocratic system itself. For example, even if a first generation of political elites are the most meritorious people available, as a class they have an incentive to establish a hereditary aristocracy that does not consider merit since it leaves them and their families as a whole better off.
Historically, for example, immediately following the Norman conquest of England in 1066 CE, the aristocrats put in power in that system were military officers who had proven their merit and been promoted by their superiors as a result in the Norman invasion of England and previous military campaigns by the Normans. But, once those individuals were put in aristocratic offices on this merit basis, subsequent holders of those aristocratic positions of power were installed on the basis of the hereditary principle rather than merit, which over many generations caused the class of aristocrats to drift from the class of people who were most meritorious in the society.
Some hereditary systems in which aristocrats have real power that have continued to function well, in contrast, such as the absolute monarchy of Saudi Arabia, try to limit these potentials for abuse and degradation of leadership quality over time by mixing the hereditary principle with a principle of merit selection within a large class of potential leaders who are all part of a large extended royal family, in an effort to prevent incompetent people with royal blood from gaining power. Thus, in the Saudi system, a talented aristocrat in a "cadet line" can be appointed to a position of power and succession by an existing monarch or council of senior royal family members, over the person who would be entitled by right to take power in a European system royal succession system in which the eldest son is automatically the heir to the throne or aristocratic post. Of course, since this system limits positions of power to members of the royal family, it excludes competent people outside the royal family who might have been preferred for positions of power on a meritocratic principle.
Meritocracy Is Hard To Put Into Practice
Another, less fundamental, objection to meritocracy, is that merit as a concept is not particularly well defined or easy to operationalize in a fair and economic manner.
Meritocracy can also fall victim to the Peter Principle (promoting people to their level of incompetency resulting in bad management) and the Dunning-Kruger effect (incompetent people overestimate their competency while competent people underestimate their competency) both because self-advocacy can be confused with actual competence and because people deciding who has merit are overconfident of their abilities to do so, again causing merit to be inaccurately implemented.
For example, critics of Human Relations Department involvement in nominally meritocratic hiring systems (both in government and in large and medium sized businesses) argue that HR employees don't have particularly great merit themselves which impairs their ability to evaluate the merit of prospective employees who have more merit than they do.
