First, by 'self-refuting' I mean it contains a contradiction within itself, meaning it cannot be true. So, if I gave instructions saying, "you may only eat apples, but sometimes oranges," that is a contradiction and thus self-refuting proposition.
The reasoning for Sola Scriptura (SS) being self-refuting is as follows:
(1) SS teaches (in a nutshell) only teachings derived from Scripture are binding on Christians.Now, Catholics don't believe SS is taught in the Scriptures, so we would say it's self-refuting. However, many Protestants fall prey to item (4) unintentionally by effectively saying "Sola Scriptura doesn't have have to taught in Scripture to be true." Most don't phrase it in that way, but it often comes in the form of "Scripture is an authority, and I'll take it as my only authority unless someone (e.g. a Catholic) steps up and demonstrates another inspired authority." That, however, is merely a variation of "SS doesn't have to be taught in Scripture."
(2) SS is a teaching binding on Christians.
(3) Thus, SS must be taught in the Scriptures.
(4) IF SS is NOT taught in the Scriptures, there is a contradiction with item (1) - thus it's self-refuting.
Another popular variation of this fallacious argument is when the Protestant objects on the grounds that for them to 'prove' SS they would have the 'unfair' burden of proving a "universal negative" (i.e. the Protestant must prove no other inspired authority exists in the world, leaving Scripture as the 'only' verified authority). But the Protestant isn't ever forced to do this, and no Catholic who understands the issue is asking them to do this, and that's because it's a fallacious argument to begin with. Sadly, this argument is often employed to shift the burden of proof off of the Protestant, but shifting the burden of proof is dishonest and fallacious (even if unintentional).
The line of reasoning where SS is 'assumed true unless proven otherwise' is at most 'negative proof', and clearly falls into the self-refuting category, for one is starting off assuming the teaching rather than getting it from a divine mandate via the Scriptures (i.e. 'positive proof').
Lastly: A Protestant can say Scripture teaches SS, at which point they wouldn't fall prey to item (4), though they (still) shoulder the burden of proof to prove Scripture itself teaches SS.