Analyze (verb) means “make an ass of.” While stating it more politely makes the origins of the word analyze less obvious, a more polite way of stating its meaning is to say that it means “make a fool of.”
Often, rather than one person analyzing another person, someone will analyze himself or herself. This is because humans have a natural tendency to make fools of themselves. It’s in our genes. Honest. Look it up.
Where, exactly, can you look up the asserted fact that a tendency to make fools of ourselves is in our genes? We don’t know all of the places, but one example of where you could look it up is in the preceding paragraph. We said it there, in case you didn’t notice.
There are a vast number and wide variety of ways to do so, but analyzing oneself (i.e., making an ass/fool of oneself) is often accomplished by carelessly saying something bigoted or nonsensical. People on both the far right and far left of the political spectrum tend to be particularly prone to this sort of thing. A balanced, rational, evidence-based approach to all complex issues of, as the late Douglas Adams might have said, life, the universe and everything will typically stand you in much better stead than blindly and automatically taking extreme right or left positions, but like we said, it’s in our genes. Or at least the genes of many people. <sigh>