I think you're missing a whole layer of disadvantage that does exist. You are so focused on the fact that you would have everything you need to go to uni now if you wanted to do so, despite not having had degree educated parents, that you can't seem to see beyond that basic fact.
Of course, nobody is saying that you can't go to university because of your family background. Of course you can, and if you decide that you want to, then I would absolutely encourage you to do so. Your kids will also have that opportunity too.
What we are saying is that it's still much easier to go to uni if you have degree educated parents. It's easier for lots of different reasons. Firstly, because the children of degree-educated parents typically grow up with the expectation that they will follow in their parents' footsteps - this makes it less likely that they will drop out of education to have a baby at 16, for example. Secondly because they inevitably get more guidance and support around subject choices, uni choices, study skills and the application process etc. Yes, you can get a lot of info from the Internet these days, but it isn't the same, and you still need to know what to look for/where to look etc.
When you look at the stats, first in family students still face higher drop out rates than students with graduate parents, and they are disproportionately represented in the less prestigious institutions. This reflects a level of disadvantage that is still there and should be acknowledged.
Those of us who are arguing this aren't trying to put you or your children down in any way. Quite the contrary, many of us want to level the playing field so that you and your dc can compete on an equitable basis with people who may have started out in relatively privileged circumstances. But we can only make the system fairer for everyone if we are willing to acknowledge the inequality of opportunities that currently exist.