It's not all about money either. Some parents don't even provide the most basic of advice/support for their children's education/career etc. As someone said above, it's not just the "big" costs either. It's the smaller things, like lifts, paying for bus fares, buying study materials etc. Even just sitting down with your child and talking about options seems alien to some parents, especially these days when so much information is available at their fingertips. Too many parents just leave it up to their kids to do their own research, make their own decisions, etc., as if they were strangers. I just can't fathom that mentality - it's like "bugger off, you're an adult now!". Being a parent is a life-time commitment, not just for the "fun" years of playing and dressing up!
We still give our son as much support/help as he needs, and he's 21 and has left Uni and started a job - obviously we're very hands-off, especially as he's at the opposite side of the country, but he still asks for advice, which we, as experienced adults, can give him and are happy to do! It's years of advice and support that has got him there - talking to him and exploring his interests/wishes and researching options etc to put him in a place where he can make his own decisions. Yes, there's been a bit of financial support along the way, but he's got full student loans and our financing was pretty minimal really, i.e. paying advance deposits for student flats, being a guarantor for flats, "topping up" his money for study materials, paying for train tickets for him to travel between home and Uni every few weeks, etc.
We'd been saving right from the moment he was born really, not for anything in particular, but as a "slush fund" for his future, whether that was going to be for Uni costs, or starting a business, or training in something else, or for a house/flat deposit, or whatever really. Small regular amounts for 18 years adds up to a fair chunk, especially with compound interest. VERY few people wouldn't have been able to save a few pounds a week over a long period of time! It's the cost of a packet of fags or a few extra chocolate bars, of a few less clothes or toys or whatever - hardly missed. (Yes, I know some people genuinely wouldn't have even a few spare pounds whatever they did, but most could make simple/cheap lifestyle choices!)