This argument always get trotted out, but it is not entirely true!
We live in a county with NO comprehensives, only grammars and secondaries, it is wholly selective.
There are a lot of primary pupils who are tutored and don't pass.
My DS (a long time ago - he's 32 now), passed the 11+ with no tutoring. I was a single mum on benefits in a council house, the very opposite of what was expected. Only two others in his year passed and quite a few who failed were tutored.
DD, who's in Yr9 goes to a grammar school. She was also not tutored and we are nowhere near middle class, nowhere near. Lots of her year were tutored, but again failed.
There is more children who are tutored than not, but my children prove that is not always necessary.
It's also common that if one child gets into one grammar (single sex), then their siblings tend to also get into the other. As there are richer pupils at these schools, it perpetuates the myth that money and tutoring buy places. My DS went to the single sex school, my DD goes to the other, so we've proved that myth, but it certainly wasn't due to money, privilege or tutoring, I guess they may both be quite bright.
They both have been given the opportunity to mix with children they'd never had the chance to if grammars were abolished, as the schools near the estate we live in are traditionally rubbish.