This is from JFK's speech is it not? A lot of the time, speeches and other creative texts have a lot of poetic licence when it comes to grammar, for more impact. I can't quite comment on this particular instance however, so I'll wait and see what some senior members have to say.

I remember the tone that JFK delivered this line. It is an example of parallelism with the next sentence, so the word NOT is emphasized: Ask NOT what your country can do for you - Ask WHAT you can do for your country. Yes, "do not ask" is grammatically correct, but it was delivered this way to emphasize YET another way to say the same thing.

Thank you for your comment!

Hello Ally, I don't have all your answers but I can shed a little light on the subject. Also your sentence needs a semicolon instead of the dash. This type of sentence is an example of parallelism. It is a poetic way to write sentences and it used a lot in speeches. Parallelism creates sentences that are simpler to grasp and contain symmetry, clarity and balance (among other things). Here is another example: "This is not only just what I wanted, but also just what I needed."