As well as being churlish, he is being sexist. He seems to think it is alright for him to interrupt her, but that she should not interrupt him.
I guess "acting like a lady" means deferring to men.
Here is the opinion of the expert, Miss Manners, Judith Martin, from her book Miss Manners Guide to Excruciatingly Correct Behavior:
On Correcting Others
Can Miss Manners, whose vocation, whose calling, is correcting etiquette transgressions, condemn the practice? Certainly. Miss Manners corrects only upon request. Then she does it from a distance, with no names attached, and no personal relationship, however distant, between the corrector and the correctee. She does not search out errors like a policeman leaping out of a speed trap. When Miss Manners observes people behaving rudely, she behaves politely to them, and then goes home and snickers about them afterward. That is what the well-bred person does.
The only way to enjoy the fun of catching people behaving disgustingly is to have children. One has to keep having them, however, because it is incorrect to correct grown people, even if you have grown them yourself. This is the mistake that many people make when they give helpful criticism to their children-in-law, who arrive on the scene already grown.
Miss Manners is constantly besieged by people who want to know the tactful manner of pointing out their friends' and relatives' inferiorities. These people, their loved ones report to Miss Manners, chew with their mouth open, mispronounce words, talk too loudly, crack their knuckles, spit, belch and hum tunelessly to themselves. They have bad breath and runs in their stockings. They are too fat, dress badly and do their hair all wrong. How can those who love these people dearly, for reasons that are not clear, and who wish to help them, for reasons that unfortunately are clear, politely let them have it?The answer is that they cannot, certainly not politely.
There are times, in certain trusting relationships, when one can say, "Cracking your knuckles drives me up the wall and if you do it one more time I'll scream," or "Have a mint—there's something wrong with your breath," or "What's that thing on your left front tooth?" No reasonable person should take offense at these remarks. Because they are so frank, they do not seem to carry a history of repulsion long predating the offense. Also, they deal with matters that are more or less easily correctable (although Miss Manners knows some determined knuckle-crackers she suspects aren't half trying to stop), and which it is plausible to assume the offenders hadn't noticed.
What is unacceptable is to criticize things a person cannot easily remedy or may not want to. People who you think are too fat either disagree about what too fat is, are trying to do something about it, or are not trying to do something about it. In no case is it helpful for them to know that other people consider them too fat. Even if it be proven that the mistakes of others come from gross ignorance or from maliciousness, it is not the place of anyone except God, their mothers or Miss Manners to bring this to their attention. As dear Erasmus said, "It is part of the highest civility if, while never erring yourself, you ignore the errors of others." Besides, it is a law of nature that he who corrects others will soon do something perfectly awful himself.