How does the original meaning of "but" ("outside") relate to its current 2021 meanings?

'But' moves you "outside of reach" of the logical options (e.g. I would help you, but ... reasons that move me 'out of reach' of helping you.)

In the OED, there are many senses of the word "but" defined.

Branch A. refers to "but" as a preposition, and the question here prepares us for definition A.1.

Outside of; (in later use often spec.) towards the outer part of (a house) (cf. ben prep.); (also, Scottish) along, across. Now Scottish.

A.3. brings us closer to a more familiar sense, although all citations are from Old English:

Leaving out, barring, with the exception of, except, save.

The OED writes this in a note:

In later use not distinguishable from use as a conjunction (see branch C.).

Branch C. refers to "but" as a conjunction.

C.I.: In a simple sentence, introducing a word, phrase, or (rarely) a clause which is excepted from the general statement. With the exception of, apart from, except, save.

Here is an example of a contemporary citation:

2013 Arab Stud. Jrnl. 21 96 My heartfelt thanks go to the following readers for their helpful engagement with this essay, however, none but I bear responsibility for its frailties.

Branch B. defines the word as an adverb. Sense B.2.a. is the sense addressed in the question, "only."

Nothing but, no more than, only, merely.

A note links this to senses under C.I., implying how they are related:

This use differs from that of sense C.[I] 1 only in the absence of any negative word

Here is an example citation from this sense:

2008 J. C. Quick et al. Managing Executive Health i. 15 It was beneficial, provided that the amasser of the wealth realized that he or she is but a steward.

Following this logic, we see how omitting the negative from "but" where it means "outside of" yields the sense that means "only."

It is nothing but X

It is nothing outside of X

It is but X

It is only X.