Sometimes an english speaker will insist this is a short form of 'I am not going to go'. A prediction or intention rather than an observation. As to how Czech uses the present for the the future, I will watch and learn.
Can't I omit the pronoun and say just "Nejedem"?
Nope, because "nejedem" is not correct. But you can omit the pronoun and use nejedu or nejdu.
"Nejedem" is very common, but not standard, for "nejedeme", i.e. "we are not going".
Russian: Ja ně jedu
Why is it "nejedu" rather than "nejdu", please?
"nejedu" is from "jet", while "nejdu" is from "jít".
"jít" is to go on foot, "jet" is to go by car/bus/train/horse/bike etc.
"Nejdu" is also accepted, of course.
Thank you for your kind, clear explanation.
I was then able to find all about nejet conjugation on the "wiktionary".