An identity is not a formula. The two sides aren't equal. They're interchangeable. It is completely different. All people are not the same as everyone else.
I've been asked what the women think a lot. I was asked what the women's thoughts were on Carl Sagan. It was once again a woman's opinions about having children. I hear similar stories from black friends about Chris Rock. Are you talking about de funding the police? We all look the same, but our opinions are different. A single black friend is all you need to claim a certain degree of credibility.
Identity is the central problem in chemistry. It's hard for a chemist to know what they have. Molecules can be different depending on their isotope. The number of possible variations is very high for a complex molecule.
There is a problem in human affairs. We would not want to admit that it happens more than we think. Evidence used to identify the bad guy is prone to error. According to a report from the National Academy of Sciences, forensic science is not based on science.
Eye witnesses aren't much better I imagine a lineup of little old ladies, one of them charged, with using her cane to clobber that kid on his scooter. The witnesses would be like the clerk at the co-op. Identity theft is related to that.
The only way to explain the strange outcry from the "straight white man" crowd when anyone from the "non straight, nonwhite, not-male" category gets a big job or award is to lump them into homogeneity. The more qualified member of the former was passed over for an under qualified member. The majority of both groups are average. The number of people running things should be equal to the number of people in power. That's simple math.
Well, at least the genetic makeup of the person is nailed down. It's not really. If lab error rates are all over the place and frequently unreported, DNA matches can't prove guilt. If the error rate is less than one percent, then the chance of mistaken identity is still very high.
Some people identify with what they are not. They used to be recovering Catholic, ex- husband, ex- boss, former friend. They don't belong to any group that isn't a citizen.