What was so special about Frodo?
Nothing. That's part of the point.
Now, the books do make mention of the fact that he is, in some ways, special: Fellowship makes mention that Gandalf thought him to be "the best Hobbit in the Shire" (quote may be a little off, my daughter has my copy atm). He's an exemplar, a "class act" among his kind.
But that isn't necessarily saying much: Hobbits do not necessarily possess any particular special qualities.
The protagonist of LoTR isn't wise Gandalf or heroic Aragorn or valiant Gimli or skilled Legolas. It could have been, so why wasn't it? Frodo has at best modest amounts of those qualities, or at least in comparison to the other central characters.
Part of the point Tolkien is making is that in contrast to the heroic virtues of cultures past he's highlighting the nobility of the willingness to pass on the temptations of power, and the willingness to sacrifice oneself for friends and/or the greater good. Doing the right thing when it costs you is more important than being good with a sword. Contrast this take with say, Homer's Odyssey.
The influence of Tolkien's devout Catholicism on the themes of the work is no doubt worthy of a greater exploration, but hopefully the ties to teachings of the Bible are at least somewhat obvious.
It's also worth noting that Tolkien seems to consider the more classically epic virtues worthy: the characters embodying these traits are portrayed rather positively. But when push comes to shove and faced with moral compromise as the price of power we see the deliberate contrast between Boromir who's epic virtues did not save him and Frodo who despite being small, weak, and inexperienced made the right call.
In keeping with this theme, to me the single best change the movies made was the scene towards the end of Fellowship where Aragorn passes up the chance to take the Ring and takes on impossible odds in a last-stand effort to allow Frodo to flee with it. Although not in the books, that scene reinforces one of the central themes (as I've argued here) of the work: Aragorn isn't great because of his woodcraft or swordsmanship but because he makes morally correct choices even when it would be more "wise" not to.
I realize the question is looking for more of an "in universe" answer, and maybe the text could even support that, but it would be of minor importance compared to the out-of-universe thematic choice.