It's an infinitive without "to", and an imperative. Why not? Many hundreds of English examples can be given: (you) resign from 20th... . (you) take the phone call. (you) watch the door. Find the nail. Press the button. Follow the others.....

It's being used as an imperative. It's the same form as the bare infinitive. He is telling her: "Either fly with me, or resign from ... [do something impossible]" It's a figurative use of "resign", which is normally used for making a choice to leave your job. She has no opportunity to "resign from the twentieth century", and he knows it. He is offering her no choice, making no concession or compromise with her on how they live, and not even pretending to pay attention to her needs or wishes. Not a good husband, some might say; he is showing the characteristics of a controlling bully. https://dictionary.cambridge.org/dictionary/english/resign https://www.laurarichards.co.uk/coercive-control/ https://en.wikipedia.org/wiki/Imperative_mood#English https://en.wikipedia.org/wiki/Imperative_mood#Formation

It is used in the imperative form. He is telling her to make a choice between two options: (1) take flights on airplanes, or (2) leave the 20th century (and go to an earlier time period when there were no airplanes). Basically, he is saying that if she wants to live a normal life (during the 1900s and afterward), she has to overcome her fear of flying because airplanes are everywhere, used all the time, and they are an unavoidable part of life.