English translation:
should not do, must not do
Structure
Verb + べきではない
I’ve also seen this used without the は (e.g. 「言うべきか、言うべきでないか」 in this chiebukuro question). Is this usage standard Japanese? If so it would be nice if you were to include it in the grammar point. 
@pampel Thank you for your question. While は can be omitted, less emphasis is placed on the negation with its absence, and answers with its inclusion (or じゃない) are generally more common in modern Japanese. I have included a note about this on the grammar page and have added でない to answers that throw hints/warnings rather than marking you wrong. Cheers!
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One thing that has always confused me with this grammar point is why it’s べきではない instead of ないべきだ. To my English brain, it’s the latter that seems correct, as opposed to the former (“not obliged to” vs. “obliged to not”). I understand that it’s wrong, but I don’t understand why.
Anyone have any insights?
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It’s actually super simple: べき is an auxiliary verb that comes from べし’s attributive form.
It sounds advanced, but it’s basically saying that it’s a verb that got turned into a noun-like word for better connection in the language. (And hence, why it’s negated as じゃない/ではない)
With this in mind, it’s just a matter of the language being in order to function.
Verb + Auxiliary べき + Negation of the Auxiliary ではない
You can’t negate what you haven’t established for negation!
ないべきだ would translate as “Don’t must.”