"No wonder that grammar is generally so poor when the privately educated are so useless at it."
Think about what you've written....
Firstly, it's a sweeping generalisation - you make the assumption that 'the privately educated' are all bad at grammar, and that can't possibly be true.
Secondly, you say 'no wonder' that grammar is generally poor when the privately educated are so useless at it. What possible connection can there be between a poor general standard and the fact that some privately educated people have a poor command of grammar? It's a nonsensical assumption to assume that one follows the other.
Thirdly, for goodness sake, does it matter? Worry about something that's really important, not this that isn't.