Well if you saw other cues to think she was embarrassed you didn't say that, as it's written sorry but it came across as textbook projection. To me it's like if someone corrected my latin at Mass because they thought I was embarrassed by it, I would thank them but they've projected a worry they have onto me.
For the record I assume that you saw other cues like fidgeting or her expressions so she probably *was* embarrassed and you did a good thing, but you did hand me a good example on a platter so I used it. Though even then, many false positives with that approach. For example, if I was grieving my grandma and an helpful lady at church assumed that my unhappiness and stress was because I don't like my borrowed missal that'd be the cherry on top.
I actually think that real empathy is rare with men too, men are very far from a paragon of empathy and do these same projections and sympathy, what I'm pushing back is against labeling women's lazy egocentric projection and poor emotional regulation as the marks of their "much higher feminine empathy".
And if you wanna see another case of false positives being harmful, tell me if this sort of thing doesn't happen all the time: imagine Justinian's church friends meet her ballet-practicing daughters, after a few meetings one of them, who verily hates ballet and is heavily projecting, says to her with total earnesty: "Hey, your little daughter N., I see her and I empathize with her and I can just tell the ballet is messing with her and her self-image" and it could be hallucinated or have nothing to do with it, and everything to do with teenagehood.
And same thing with any such social policing.
You'll see that most men don't tend to bring up some sort of nebulous secret intuition to socially police you, they'll just tell you things and arguments, and those range from true to nonsense, but they aren't "I just get the distinct feeling that you're wrong and it's hurting you"