It is not. In a meritocratic system, children wouldn't inherit resources, access to education would be conditioned purely by merit, and so would access to jobs, finance opportunities etc.
The nepotism rampant (edit: was "inherent") in corporations, government, the finance industry etc. are exactly the things that keep the rich rich and the poor poor.
- society (through local community funds etc) would ensure that everyone, regardless of anything else, has access to basic livelihood (food, shelter, clothes, transport, healthcare)
- society would ensure that everyone has access to the same educational institutions, including required resources (manuals, computer access etc.)
- people would strive to evaluate others based on actual aptitude, rather than class markers (e.g. someone speaking with a heavy "uneducated" accent or wearing low quality clothes wouldn't be looked down upon being evaluated for a professorship or top management position)
- inheritance would be heavily taxed; this would be set up in such a way that people would have a right to the human elements of inheritance - e.g. the home where they grew up, their parents' memories etc. - but huge transfers of wealth, such as inheriting your parents' Amazon stock would not be profitable.
Better off parents will still be able to give a better life and resources to their children, but the impact of that care on the ultimate outcomes will be much less. A "perfectly meritocratic" system would likely be horribly dystopic, such as entirely separating children from parents at birth, Brave New World style.
A good public education system goes a long way. At the moment in the US, rich kids benefit not just from the education their parents give them directly (which let’s face it is not necessarily that great just because they’re rich - how much has Ivanka benefited from Donald’s insights?) but also from the expensive schools that their parents can afford to send them too. Educational apartheid by wealth isn’t a necessary feature of a society. It can largely be legislated away given the social and political will to do so.
It is a fundamental feature in class-based societies like USA, the UK and much of the rest of the Anglosphere. Maintaining the class structure and preserving the accrued intergenerational wealth from the upper strata of society means that the kids of those wealthier classes must acquire distinctive social manners and culture which sets them apart from the commoners.
Maybe aspirational, but it's not reasonable to expect this.
More educated parents both earn more money and educate their children more (and not per se due to their higher earnings).
It's hard to compensate for that.