You could say the same about food if you take that attitude. Knowing how to cook from scratch from simple ingredients - are you cheating at their nutrition over those who only buy ready meals? Of course not.
No you really can't. Teaching your child to cook is broadly accessible to everyone, and even if it wasn't, a child could teach themselves to cook when they're older, and it's unlikely to be the key determining factor in determining the course of their life. Furthermore, if one child can cook, it doesn't stop someone else from cooking (it's not zero sum).
However, with private education, it is not open to everyone, and it's likely to have large impacts on your child, at the relative expense of someone else (there is some degree of it being zero sum, because there are only so many places at Oxbridge, medical school, and only so many legal training contracts).
This is what I mean about owning it. The deal with private education is this:
Pay £X,000 per year. We will increase by X00% that your child will be offered a place in law school, Oxbridge etc, and push your child ahead in the queue. This is at the expense of those who can't afford these opportunities.