Grammar: 食べないんです vs. 食べません
The Feeling module has the sentence
どうして あさごはんを 食べないんですか
which is translated as "Why aren't you eating breakfast?" I have not encountered the nai-form + です before: why would one use it, rather than たべません?
Also, is translating this as present progressive really appropriate? Wouldn't one need the te-form + いる for that?
食べない and 食べません mean exactly the same thing, except the former is the informal dictionary form and the latter is the polite ます／です form that's more appropriate for strangers and people situated above you socially (e.g. your teacher, your boss, etc.)
The real difference here isn't ない vs ません. The difference is that tiny little ん between ない and です you probably didn't even notice. The んです is actually a contraction of の+です. When placed after a verb in dictionary form, の nominalizes the verb and its clauses, meaning you can treat the relative clause headed by the verb before の as a noun phase in the surrounding sentence. This has many uses, some of which you will see later on in the skill tree.
Now, this hasn't exactly answered your question. Why on earth is it useful to turn 食べない into a noun with ん／の just to end it with です? It creates emphasis that the statement is a fact or the current situation. 食べません is a fairly neutral statement, simply meaning "(you) do not eat", whereas 食べないんです is more pointed, meaning something more like "it is the case that (you) are not eating".
Therefore the full sentence in the provided example 「どうして あさごはんを 食べないんですか」 could be translated a bit more accurately as "why is it that you are not eating your breakfast", which makes a slightly more pointed question than the neutral 「どうしてあさごはんを食べませんか」 ("why aren't you eating breakfast"). I'm not sure I can properly explain the intonation it adds in every case, but in this situation it shows interest in the lack of apetite of the person you're talking to.