grammar - How to say regrets [I should not have X]

How in the world does this:

晩ご飯を食べるんじゃなかった。

translate as "I should not have eaten breakfast"?
This roughly translates as "It was not that I eat breakfast."

Answer

First and foremost, 「晩{ばん}ご飯{はん}」 means "dinner", and not "breakfast".

Next, let us study the present-tense form of 「～～んじゃなかった」, which will naturally be 「～～んじゃない」. This might give you a clue.

In colloquial speech,

「Verb or Verb Phrase　+ んじゃない！」

expresses prohibition. In other words, this is an informal negative imperative.

「ひとりであの公園{こうえん}に行くんじゃない！」= "Don't go to that park alone!"

It is imperative (no pun) that you be familiar with this present-tense usage in order to get a feel for the past tense-usage.

「Verb or Verb Phrase + んじゃなかった」

expresses what I might call "retrospective prohibition". In the plain word, it would be "regret".

If the sentence "I should not have eaten dinner." expressed the speaker's regret or repent, then that would be an excellent translation of 「晩ご飯を食べるんじゃなかった」.　

This roughly translate as "It was not that I eat breakfast."

No, it does not, I am afraid.

「食べるんじゃなかった」 surely talks about the past, but the past tense is expressed in the 「なかった」, not in「食べる」.

TL;DR:

「食べるんじゃなかった」 = "I should not have eaten."

「食べたんじゃない/なかった」 = "It was not that I ate." ⇒ "I did something else."

First sentence says "I ate." and the second, "I didn't eat.", so the difference is huge.

Once again, be reminded that this is all colloquial speech.　In more formal speech, one would say;

"I should not have eaten." = 「食べるべきではなかった。」