There's a debate between her and Boris Johnson on youtube arguing the Romans vs the Greeks and he makes her look like an amateur both in delivery and content of her arguments

I think people dislike her because she’s informal and popular in talking about a subject which is traditionally elite. She talks a lot about ordinary lives rather than great events, and she presents herself as an ordinary person, wearing trainers, with normal hair and teeth. A lot of it frankly is that she is not young and doesn’t attempt to make herself up to look young. You can see in many places there are very few women over the age of 50 on TV who have not been heavily made up.

All of this could be thought of as progressive or left wing but not in a way which anyone should object to! The only reasonable criticism of her I’ve seen is the discussion around the “ordinary British family in Roman times”, which was obviously wrong but made an underlying point which was valid, i.e. the lack of a modern idea of race in Roman civilization.

I think she has also objected to some aspects of gender self-id which would apparently make her right wing in a US context.