is it dabei because "ich mache bei etwas mit"? If so it's confusing that it's mitmachen bei but teilnehmen an
In this exercise, "dabei" looks to be the literal translation of "in that". Could it be as well a literal translation of "there"?
Possibly because your version just means you don't agree to something (going for a meal?), but the original means you don't want to join in something (a football game?)
I think "I won't participate..." should be accepted. "I won't.." also has the sense of "I don't want to.." or "I refuse to ...", not just simple future.
I got marked wrong for submitting "I do not want to participate". I know there is an additional word in the German ("dabei") that indicates you don't want to participate in something specifically, but the English word "participate" already implies the "in that" part. You can't just blindly participate, you have to participate in something, so adding "in that" is a bit redundant.
I wrote "I don't want to participate with it" Marked correct, but somehow I don't think this is correct English.