「わけ」 (「訳」) originally meant “to divide/separate” (related to 「分ける」 and 「分かる」)
consider “breaking something down” to make more analyzable and understandable
「わけ」 expresses a cause, a reason, a conclusion, or a logical judgement (the underlying causality or reasoning)
reasoning can run forwards (looking at past events to reason about the current situation) and backwards (looking at current events to reason about how they came to be)
ex: 「そういうわけでベッドの下に隠れた。」 means “That is the reason why (I) was hiding under the bed.”
ex: 「そういうわけでした。」 means “That is the causality for what happened.”
the causality happened in the past, not the reasoning
ex: 「そんなわけで宿題を忘れました。」 means “Such a thing is why (I) forgot (my) homework.”
ex: 「わけが分からない。」 means “The underlying reasoning does not do analyzed.”
ex: 「お金が足りないわけではない。」 means “Lack of money is not the reason.”
「お金が足りない」 is modifying 「わけ」
the construction 「○○=○○わけではない」 tends to imply that the first proposition does not have the reasoning of entailing the second proposition
the construction 「○○わけ(が)ない」 tends to deny that something exists
「○○」 does not have any reasoning and is therefore not true
ex: 「田中さんは嘘をつくわけがない。」 means “Tanaka-san would not tell a lie.”
“The underlying reasoning of Tanaka-san using a lie does not exist.”
「わけがない」 can also be used to say that something exists without reason
ex: 「そんなにお金のいるわけがない。」 means “There is no reason for the need of that much money.”
「わけ(が)ない」 can also be used to say that is simple
「○○」 has no reasoning and is therefore simple enough to exist without it (hyperbolic construction)