What is the support behind the notion that if your parents are middle class, you're likely to grow up to be a middle class adult?

I was talking to adults and this topic came up. There were not a lot of supports for the claims but the claims essentially stated that although you can of course work hard and do something to get out of the class you're in, for the majority, white collar parent's kids will be white collar when they're adults and same with blue collar parents and their kids. Why?