Am I being unreasonable about being offended when people think men should sit at the head of the table?

No point being offended, I'd let it go, and just enforce on my girls, that they are valued and just as important, but as for the table thing, I wouldn't make a big deal out of it.

Perhaps suggest that your MIL sits at the "head" of the table as she is the guest. I have just realised that DH sits at one of the short ends of our long rectangular table when it is just the 2 of us....I sit to his left at one end of one of the longer sides - I have just realised he is at the "head" of the table - really it is of no issue.

It’s your MIL who's the issue here , not so much the outdated tradition where men were sat at the head of the table .
You told her why you didn’t seat him there , your table is a rectangle with 3 chairs on each side but she chose to specifically move one chair and set him a place there .
In our house ( I have 3 daughters) we sit wherever is comfortable for us .
Eg I’m small and don’t have much padding on my derrière so I do prefer one particular seat.
DH has long legs so needs to sit wherever the table isn’t going to knock his legs and ankles ( we are considering getting a new dining set for our kitchen dining so need to take this into consideration )
Also I think whoever is getting up and down from their chair the most , for whatever reason ( checking on food cooking, getting extra portions ) needs to eg the one who has the seat that’s easier to move from and access the cooker etc

It’s not an issue unless it is designated the head of the table, but in this instance MIL made a show of the man being the head of the table by calling it that and moving his seat and place setting. If your DH hasn’t declared that he is head of the table and you have to do everything food (and household chore) related then it isn’t an issue

Same as @accidentalmillionaire my MIL came to visit and I was just about start plating up the dinner when she said” serve the man of the house first”(her son my XH).

I remember replying to her”in this house children are served first then guests and the man of the house can wait his turn”.

She was shocked by my non-compliance but that’s the way she was brought up and she (probably like million others)never questioned it.

Is all this driven mainly by handmaidens wanting to find a token way to make women subservient to men, or is it pathetic misogynistic men who expect or feel flattered by it... or both?

I can't imagine anybody older than about 6 or 7 remotely caring about being given a chair/place that's just the same as all of the others but which is nominally dubbed as 'the special one for a special boy/girl'.

Definitely overthinking it!

My husband sits there to stop the kids fighting 🤣🤣

And that’s fine. But moving chair and place setting just so he can be head of the table as he is the man and for no other reason is not good

The head of table stuff is anachronistic, like men getting up at the table when a lady gets up or when she enters a room. Or men opening doors for ladies. Very Downton but not exactly a hanging offense.

Also the old one of a man publicly taking the blame when a woman farts loudly, 'to spare her embarrassment'.

You’re underthinking. Mil isn’t putting him there to do anything useful. She’s putting him there to symbolize his ownership of and control over the household, though I’m sure she wouldn’t say that out loud.