It's pretty easy with jede (same as with many other words too): Masculine = jeder, Feminine = jede, Neuter = jedes. Jeder Hund, Jede Katze, Jedes Kind and so on. In this case: AFAIK it is a common phrase for "not everyone" and for some reason it requires the masculine. (Just guessing, but it might be that the "original" phrase was "nicht jeder Mann")
Hm. I write "Not everyone" and it says I forgot the space, I write "Not every one" and it says you have an extra space. Make up your mind, bro! :D
I am totally confused by all these words. For example what is the difference between jeder and jemand?
In my german grammar, jeder/jede/jedes/jede correspond to 'each', while jedermann to everyone. Perhaps in this example jeder is taken as an abbreviation of jedermann. I hope this is right and helps someone.
Also, jemand is 'someone' and niemand is 'no one'.