Each of us carries numerous identities as a human. One person may have significant identities that are oppressed as well as privileged. For example, maybe you are a Black, Christian, woman, born in an upper middle class family. Some of those identities will come with privilege, others with oppression.
There are commonalities to all our lives as humans: loving, working, taking care of your family, etc. If you identify as a person of color, all of these events might also be affected by the systemic racism in our society. The same is true if you identify as LGBTQ - you might feel the oppression of homophobia. So a break-up will not only contain the struggles that come with any break-up, but may also contain the hurts that come with racism, homophobia, classism, sexism, etc. Whereas if you are white, straight, middle class, you might not have to think about the color of your skin, your sexual identity, work or money or how your personality was shaped as a raised poor person. That is privilege.