This expression of inevitability is a glowing ember of the teaching of Latin in the 18th ad 19th centuries to boys and some girls in well-to do families. And of all the features of Latin that they dreaded, the worst were the two words 'quominus' and 'quin'. They introduce subordinate clauses expressing prevention, impossibility and inevitability. And the worst of these syntactic beasts is that there is no possible way of translating either into English that does not look a bit weird.
Quin (followed by a subjunctive) is the worse of the two. The most familiar (to victims of Latin) example of its use is the expression
Nemo est quin sciat.
It means 'everybody knows'. Literally, this simple English clause is saying
There is nobody such that he would not know.
But the teachers and translators picked as the subordinating conjunction the expression 'but that' and offered their readers and schoolboys the literalistic translation
There is nobody but that (he) knows.
And it caught on. It became clear that anyone speaking like that was properly educated - had mastered the dreaded quin.
The use of but was not as crazy, however, as I have made it sound. There is a well established concessive usage of but as a preposition, meaning except or other than. So a parent might grumble
My daughter is friendly and talkative with everyone but me. So The Cambridge English provides definition
But preposition, conjunction B1 except - with the example
This car has been nothing but trouble.
And it gives examples of this subordinating use of but as a conjunction:
in these cases there is no choice but to amputate (which would go straight into Latin as quin amputarent and get forced into English by 19th century (and a few 20th century) Latin masters as but that they might amputate.
I think the Cambridge English definitions will give you the detail you need [www.dictionary.cambridge.org/grammar/british-grammar/but]