In your example, the question really is, “Why isn’t he (going to the station)?” However, since the first speaker said, “He is not going to…” the second person can simply say, “Why not”; likewise, if the first person said, “He is going to the station two hours before the train arrives,” the second person could ask, “Why is he?” We mostly use “do” linked with actions: so if I say, “I can’t go out tonight, I have to do my laundry” another person could reply, “Why not do it tomorrow instead?”

So besides "why not " , is it possible to use "why not do...." Because is an alternative to "does" or "do". To do, is generally, an "action". So, "why not" does not always offer an action as a possibility. For example, if the other alternative is a new way of THINKING about something, I would not say; "Why not do______________". I would say instead; "Why not THINK of it this way?" So "do" can be awkward to impossible for such an alternative. I can talk or write about doing Something or Nothing. But THINKING or UNDERSTANDING or FEELING are not typical of actions in English. In reality, we do think, understand, or feel. The critical distinction can be seen in Science in what is termed The---Causal---Relation. Thinking does not change physical things. Therefore, thinking is not "doing" you see. Thinking has no physical effect, so it is not "doing".