One, of many reasons, why people have difficulty with "generalizations" in these types of conversations is because they do not consider themselves as having a group identity. White Americans is a group identity. It is a useful group identity for discussing shared/similar lived experiences, cultural features, power and privilege, relationship to systems, etc.
But a lot of people, not just White Americans, see their lives solely through an individualistic frame. They do not consider themselves as part of a group, a society, or even a culture. I have had students tell me that they reject the idea of there even being such thing as White culture. And yet, these same people who do not see themselves as part of a larger group or culture tend to have no problem seeing others through their group identity such as Asian Americans, African Americans, LGBTQ Americans, women as a group identity, etc.
The truth is we do have group identities and shared cultures. There is a way of looking beyond the individualistic frame that helps explain people's different relationships to power and privilege. But for some, the inability to see beyond an individualistic frame shuts down all conversation. They only see themselves as 1 person, not a member of a larger group of people with similar and shared features.