Guilt is useful if it can change behavior. Its not useful if there is no behavior to change.
I cannot change my being white. I'm not aware of anything that I am doing that oppresses people, rather the reverse in fact, I'm involved in some programs at work that are targeted at providing opportunities to people who otherwise would have fewer opportunities.
I can't change the fact that I get certain advantages from being white. My whiteness does not give me some special power over society. I can only change how I behave to reduce the oppression of others.
Imagine I was trying to get paternity leave rights for men in a place where they already existed for women. Wouldn't it be far better to say that men should have the same rights as women with respect to leave, rather than "women need to accept that they get *special treatment* for leave". The goal is to give everyone reasonable treatment, not take it away from those that have it.
These conversations get confusing because the opposition to "privilege" is composed of at least 3 groups:
One group does not believe that there is any remaining bias in society. The will reject privilege or oppression arguments out of hand.
Another group believes that there is bias and generally would like to fix it. They are much more likely to respond positively to request to help stop oppression than accusations of "privilege".
A 3rd group is "white", and so has been labeled as "privileged", but in fact is not. They are suffering from a variety of oppression not based on race, but on some other issue. They may be very sympathetic to the oppression of others, but are not going to react well to being called "privileged".
Words matter. Saying person A is privileged, is different from saying person B is oppressed, even though both imply that A is in a better situation than B. The difference is which situation is implied to be wrong.
And what is wrong with that?
What happens when we feel guilty?
Do you ever apologize to your wife?
Do you ever feel guilty about something you did?
What happens as a result of feeling that guilt?
We become aware of ourselves and avoid repeating. We also apologize, or we're supposed to. I know many in the population who simply cannot apologize and think it is a sign of strength. It's not strength. It's the opposite of strength, weakness. You fear apologizing might make you look weak. It is that fear that makes you a weak person.
Only you can answer the rest