That is only true to a certain extent.

The environment they are exposed to is a huge factor.

If a child grows up being given opportunities to learn and sees other family members who read, do things for themselves, figure things out and solve problems then they are more likely to do that themselves. If, on the other hand, they aren't given the opportunity to learn to do things for themselves (ex: mommy puts their coat/shoes on them because it takes too much time to let them learn to do it for themselves) and if every person they see sits on their ass eating bon bons while staring at the TV then that's what they will likely do themselves.

Yes, each child is different and will learn at their own pace but it is the responsibility of parents to expose their children to learning opportunities, to guide them to learn to do things themselves, to set examples and to provide them with a stimulating environment constructive to learning. This can be as simple as making counting games, letting them learn to measure by helping you cook, teaching them to sweep up messes and dress themselves - all these things develop fine and gross motor skills, hand-eye coordination, foster self-esteem and a sense of independence. The learning of math and reading skills can be incorporated into nearly everything. It doesn't have to be formal lessons - and shouldn't be.

Barring those with disabilities, there are things that every child by age 5 is capable of doing - such as writing their name (actually by 3.5 every child is capable of doing this provided the right environment). If they have not been provided the opportunity to develop these skills that is a failure on the part of the parent who, imo, is too lazy to teach their children and leaves it to the schools. Most learning should happen in the home, imo.

Children have sensitive periods where they are better able to learn things, they will learn them with ease and at a faster rate during these times. The sensitive period for language is nearly over by the time most children start school. Yes, most will still reach a level where they will be literate but an opportunity for them to start with a good foundation and build on it will have been lost. Children who learned the letters, the sounds, word building and reading beginning at age 2.5 fare much better all during their school years (including college).

The most important thing to learn at that age, and the factor that most determines how they will deal with all aspects of life in the future, is for them to learn self-reliance, gain self-esteem from learning to do things for themselves, and through doing that learn to deal with making mistakes, how to know when they've made a mistake, and how to correct their own mistakes.

If children don't learn to read and write at home then they certainly will learn at school - most of them anyway.

I think most people try to teach their children something before they turn their education over to strangers though.

The problem is that most children go to school at age 5 or so and by then so much opportunity has already been lost. Opportunities for learning and developing positive attitudes toward learning (as well as self-esteem and independence) that will never come naturally again, at least not at the same levels. It is not too late for children to learn to read, write, and do math by any means, but the sensitive periods - where they would learn the most, the quickest and enjoy learning the most will have passed.

More importantly, the best opportunity to develop 'normalization' - the ability to concentrate on tasks - is long gone. That's not to say those children will never learn to concentrate - just that it won't be as easy for them as it will for children who were given the opportunities to develop concentration from age 2 or so.

We're not talking about something that only affects the first year or so of schooling. These things have an effect for the entire life of the person.