alc.co.jp seems to be a very nice website that I just bookmarked. There are a lot of kanjis but they are using simple Japanese.
いいえ、まだ食べていません。Emphasis is put on the current state (of the conversation). Well at least this is what they want to say by 現在の状態.
いいえ、まだ食べません。Emphasis is put on the fact that whether the action is over or not, has been accomplished/realized or not.
On the first part they are saying that for this question:
They say that this answer is correct if the answer is talking about a certain time in the past. For example you could use it to say: I wasn’t there at 7pm: 7時にはいませんでした。
However since the hidden meaning of this question is «You were not back home YET yesterday». You cannot use いませんでした and have to say いいえ、まだ(帰って)いませんでした。
When asking this question:
もう読みましたか? Have you read it yet?
All those answers are correct and adapted to the situation. But what’s the difference then ?
Well here the difference is whether you want to continue talking about the fact you read your book or not.
You could say for example: まだ読んでいないので、ニュースを知らない。
If you say まだ食べていません, your friend could answer じゃ、おなかがすいたでしょう。
This is a summary of what this article is saying which is true however is that really helping your understanding? I don’t think so. Here is my version:
When you are talking in Japanese you are always saying things implicitly, but Japanese know that so they won’t talk about those implicit meanings.
If your friend asks you もう昼ご飯を食べましたか and you answer まだ食べません, that might be correct grammatically but that’s rude.
It’s like: Have you already eaten lunch? yo I don’t eat yet in a polite way (まだ食べません).
However if your question is もう昼ご飯を食べる時間ですか? (Is it already time to eat lunch?) you may answer まだ食べません (We don’t eat yet).
The important detail to me is the difference between まだ食べていません and まだ食べません which is 食べていない and 食べない.
食べていない is the negative from of 食べてる. 食べてる means « the fact of being eating » at the moment which means I am eating right now. Well that’s the contrary ? « the fact of not being eating right now » (I’m not eating right now). If you add まだ you are basically adding « not yet » to the sentence, negative + negative = positive so まだ食べてない means I haven’t eaten yet. (I haven’t realized the action of « being eating » yet which means I haven’t eaten yet). This form is like present continuous in English.
食べる may be used to talk about the present and true facts. For example: It’s a fact that it’s not the time to eat right now.
So if you have already eaten you would answer もう食べた because that fact is over and not もう食べてた.
If you ask 11時にもう食べてた? (Were you already eating at 11am?) you have to answer もう食べてた because the fact was not over at 11am, it was still happening.
If you understand the true meanings and differences of 食べる, 食べてる, 食べない, 食べてない, picking one of those will be obvious.
This is all about context. If a girl asks you at 12am もう昼ご飯を食べましたか? and you answer まだ食べません. This is about the present and/or true facts: right now I don’t/won’t eat, it’s a fact I don’t/won’t eat now. She might think for example you don’t want to eat it / you don’t want to eat with her / you can’t eat right now.
However if you answer まだ食べてない there is no misunderstanding possible, you open the door for her to ask you out for lunch.
About the examples in the article :
A : いいえ、読みませんでした。: I didn’t read it.
B : いいえ、まだ読みません。: « I don’t read it yet » (which doesn’t really mean anything). Again this is about present or true facts. Right now I don’t read this book, I won’t read this book for some reasons so maybe you don’t like this book and you don’t want to read it.
C : いいえ、まだ読んでいません。: I didn’t read, but you imply that you are planning to read it, so it means you want/have interest to read this book.
Here answer B is fine because you are talking about a book, you are not answering to a person, you can’t be rude to a book.
So I think you should definitively answer いいえ、まだ食べていません。whether you continue your sentence or not, that's what people use 99,99% of time.