I do think a lot of people get riled up because they hear the term privilege and think you are 'accusing' them of other types of advantages which they didn't have
To me white privilege is basically if everything else is the same the white person has the advantage
So two kids growing up on a council estate to a single mum where the father isn;t involved in their life - neither has much advantage in life - but the white kid (A) doesn't face the additional difficulties faced by the black kid (B) (increased risk of being stopped by police if they are both hanging round outside the local shop)
Two kids growing up middle class on the same estate, two parent families, go to the local school (same one) get the same grades, go to uni and study the same subject, both come out with a 2:1 - the odds are if they interview for the same job and both are equal with white guy (C) will get it due to subconscious bias - ie the black guy (D) has to prove themselves more - it doesn't mean they can't do it, but it is slightly harder)
Two more people (one black (E) one white(F)) grow up as the children of millionaires, they both go to Eton followed by Oxford and follow Daddy into the family business - both are extremely privileged but if they are both out jogging late at night around their local area the black man has far more chance of being viewed suspiciously but those who don't know him
Person F has the highest advantage of all of them, he's got family money behind him, a private educate and he's white, person E has more advantage than people A-D but not as much as person F
Person B is at the bottom of the advantage pile - has everything stacked against him - thats not to say he won't get anywhere but it will take a lot more work and luck