"訳分からない" various uses of 訳

Question

Here are a few examples of 訳 that I am having trouble with:

僕は決して農業が嫌いな訳じゃない。 Boku wa kesshite nōgyō ga kiraina wake janai.
By no means do I dislike farming. (Lit: The reason is not that I dislike farming)

How does the kesshite work here and is wake best translated as reason?

わけありの二人 [ex #1268] A couple with some amorous circumstances

a commentator provided this explanation for the latter example:

わけ originally comes from the act of dividing things into what is right and what is wrong.Therefore, わけ came to mean 'reason' or the rationale of how things are done. That later got expanded to include the amorous relationship in the sense of 'there is a reason for them to be together or in love,' as suggested by #1268. any further clarification would be appreciated.

それを纏めるのはわけはない [ex #1269]Sore o matomeru no wa wake wa nai Not difficult to resolve that issue

それとこれとはわけが違う [ex #1270] You are trying to compare apples and oranges.

訳のわからぬことを言うな。 [ex #4961] Wake no wakaranu koto o iu na. Don't tell me such nonsense!

any exposition of these 3 examples would be appreciated.

Finally i saw this mentioned as a "slang term". I am not familiar with it, I was wondering if any one knows it and can explain it.:

"訳分からない”

Answer 1

"わけ" has a range of meanings from "reason" to "meaning" to "significance".

1. 僕は決して農業が嫌いな訳じゃない。 "決して" = decidedly, absolutely. "It absolutely doesn't mean that I dislike farming." More idiomatically: "It's really not like I dislike farming."
2. "わけありの二人" "A something-significant-going-on couple." It's a little idiomatic in usage, but generally "わけあり" means there's something going on, there are certain circumstances, etc. If you know or suspect something significant is behind something, and you can't or don't want to explain in detail, "わけあり" gives you an out.
3. "わけない" Insignificant = simple, easy, "a piece of cake".
4. "訳(の、が)分からない" Meaningless = Greek to me, piffle, horsefeathers, nonsense.
5. "それとこれとはわけが違う" That and this have different significance, i.e. they can't both logically fit within the scope of the discussion at hand.