But, mostly, I think "The men are eating bread." would be a better translation.
In this sentence, that translation makes a lot more sense than the generality, "Men eat bread", which is of questionable significance and meaning. Yes, men eat bread - except for those men who don't. And other people eat bread - except for those who don't. It just doesn't mean much of anything, except as a vague generality which is sort-of true.
There's context - what's going on around and in addition to what is stated in a sentence. And then there's inner context within the sentence itself. Sometimes, the inner context can suggest the better translation. Spanish example: El hombre tiene un bebé = "The man has/is having a baby." "has" is the translation of choice here.
Sometimes, the inner context can refer subliminally to an outer context. "Men eat bread" is internally consistent, and does not require some outer context for clarification - but by reference to a kind of unstated relationship to external considerations, it becomes a lot less apparent what the actual meaning of this sentence is.
"The men are eating bread" is much more specific and limited, and allows for a lot more time when they aren't eating or don't eat bread.
An example of where this distinction isn't so obvious: "Men go to war" or "The men are going to war."
Is "Men eating bread" not right? Would that instead be "Мужчины ест хлеб."?
"Men are eating bread" would be correct instead, in addition to "Men eat bread".
"Men eating bread" is not even proper English, unless you provide enough context. E.g: I saw some men eating bread.
I don't understand why it marks "The men are eating bread" as wrong. How should I say that? Мужчины едят хлеб, пока мясо на гриле.