Talking about privilege often gets derailed by people pointing out their own difficulties and pain.
There are a bunch of metaphors to try to get past this roadblock (there’s ten good ones listed at https://www.scrapingraisins.com/2018/02/ten-white-privilege-metaphors/), but they tend to not be really useful when someone (including myself) is in the middle of the difficulties that life throws at you.
I’ve had to develop a strategy to talk to myself in these situations, to really activate my own empathy using some elements of Non-Violent Communication. 
First, I take a hard look at my own problems and difficulties. I don’t minimize them; pain is not a competition. I acknowledge how much pain they cause. I listen to myself with empathy, and acknowledge the hurt and pain that exists.
Once I’ve done that, once I’ve fully and completely really stopped and sat with my own pain, do I start thinking about everything else.
I think about the advantages I have. I take the time to acknowledge the advantages I have. I list out my social, cultural, and economic capital, as best I can.
Here’s the important part: I do not think of any of those things as lessening my pain or difficulties. I make sure to acknowledge my own difficulties and pain.
Only then do I let myself consider how much more worse things would be without them.
It is a small distinction, but it is a vital one. Instead of discounting my own pain, it helps me be more empathetic by acknowledging my difficulties while realizing how much worse it is for people without the advantages that were handed to me.
Because I know how hard these things have been for me. And the idea that others facing the same kinds of problems have even more roadblocks in the way… well, that just mades me angry at the system that does that to other people.
And then it’s time to get to work.
I know the difference between acknowledgment and triage, after all.
 Still not perfect at it, but this helps.