I don't think framing it in terms of guilt is helpful, nor is trying to construct privilege as something that people should be ashamed of. It just makes people very defensive. What is better is for people to be aware of what advantages they had that other people did not, especially when they're telling other people what they should do or saying that everyone could get to their level if only they worked hard enough - hard work is not sufficient, avoidance of obstacles is also necessary.
(Private education is tax-deductible in the US? Blimey. The UK setup is slightly different - private schools are usually structured as non-profit educational charities, with tax advantages, and even that is grudgingly accepted due to the age and character of the schools.)
Did you have a computer at home as a child? That's a huge advantage that was outwith your control.