Here is a scenario, and my mac is a month old, so maybe I am borrowing heavily from Ubuntu and MS experiences. When I am reading two pdfs, and then close one, it makes sense for the preview menu to stay on because I am reading the second pdf, but when I close the second, what reason is there for preview menu to stay up?

Edit: As to my original comment, when I switch to another app, preview stays open, but up to now I don't know how to close it because I can't get the menu to appear without a pdf or something using it, that's why I reopen a document, forcing the menu to show up, then close the app.

There's lots of reasons for the menu to stay open; the simplest example is clicking File, then Open, to open a new file.

As far as the menu disappearing when you close both documents, that's confusing and directly contradicts what you typed earlier. I can open Preview.app, and it'll just show me the menu. I can close it by alt-tabbing to it and hitting Cmd-Q - no windows required.