At the moment they are not missing anything because the youngest is below the age of going and many countries don't start formal education until they are 7 yrs anyway.
After that it depends on how sociable you are and how many experiences you can give them.
I would say the main thing is a huge pool of friends that they can make without you organising, but that is assuming it would be a large school. Probably the main thing is the opportunity to see friends everyday, to cement friendships, and the opportunity to see ones everyday that your mother doesn't necessarily like. My mother didn't like my best friend so I am sure that she wouldn't have made access easy and yet she is still a very close friend 50 years later.I can't see why my mother needs to like her, I don't like all my mother's friends.
They miss having to sort out problems for themselves when things go wrong, but perhaps you are the sort if person who can stop interfering and let them get on with it.
They miss a sounding board for ideas and all sorts of different views and opinions. e.g. If you are doing maths someone who comes up with a different way of seeing things, people to play number games with on a daily basis. E.g. If you want to write a story you miss the exchange of ideas, you miss seeing what others wrote. E.g. In history you miss someone having very different views on a person or event, something that you might have missed. I mention those because it is what I found particularly exciting about school.
You miss access to the school library which is OK if you get them to the public one at least once a week.
You miss group work to do things like science experiments.
You miss access to equipment e.g if you are doing work with electric circuits the school has all the batteries, crocodile clips etc.
You miss a kiln.
You miss team games on a regular basis and a hall with climbing bars, ropes etc.
You miss visiting theatres etc who give talks and put on plays etc.
You miss a different adult who might get completely different things out of your children.
You miss being part of a wide community. You miss having a life away from your mother and the chance to only tell her what you want to tell her.
You miss being in plays and performing for a wide audience ( it depends on what groups you belong to).
You miss getting away from your siblings.
A lot of this depends on which groups you belong to, if lucky you can manage a lot if it yourself and how much effort you are going to make and how much you are happy to give independence and get paint out and have messy activities like clay and generally getting dirty.
You can do drama, dance classes etc but it will be costly, instead of free, and if you live in a rural area you will need to run a car.
You can do it all but it takes a lot of effort on a daily basis.
Secondary school is more difficult, when I think you need the specialist knowledge for the subject and the exam syllabus and the equipment problem is more acute.
Lots of people will be able to say they don't miss this, it is only my opinion.Your mistake is to explain and try and justify to people, it is not a requirement!