Ok, I suppose I understand but I really do not agree. Modern criticism of the US president is so far removed from medieval criticism of a female monarch as to be nearly irrelevant.

To address your question, though, yes I absolutely read "proper to the gentler sex" to be a statement about how Queen Mathilda _ought_ to have behaved. Also I have strong doubts that men (especially male rulers) at the time would have had the same standard set for arrogance. Of course a King could be in fact arrogant and then critics might point that out, but I do not see why they would bring his sex into it.

One thing we might agree on is that all political criticism can be false, and whether or not she was _actually_ arrogant is difficult to say. In the context of a bitter civil war, any record of events will have the strong bias of the author. The modern world did not invent fake news.