When the ring is first brought forth at the Council of Elrond, there is an instant debate, verging on starting a physical fight, about what to do with it. Some members of the council suggest it should be given to Tom Bombadil to keep safe, as he suffered none of the rings allure and temptation, but this is discounted because he would not care enough to protect it from the darkness that seeks it. Others suggested it should be hidden in the Undying Lands, out of reach of Sauron, but this too is discounted incase it poisons the last pure lands that the elves can retreat to, and is essentially like releasing sin into heaven.
The only solution left is to destroy the ring, which Gimli attempts without a single hesitation, smacking it with his axe before being sent flying. However, there is one more option that is put forward by Boromir, who argues that taking the ring towards the enemy, and essentially delivering it to his doorstep is essentially suicide, and is doomed to fail.
When put like that, the “One cannot simply walk into Mordor” and “Not with 10,000 men could you do this” starts to make a lot more sense, and the audience can begin to see things from Boromir’s perspective. Surely leaving two defenseless hobbits (Frodo and Sam) to take the object upon which the entire world depends right into the land where the greatest opponent lives, alongside a whole host of his evil creatures and orcs, as well as far more dangerous things within those lands, seems like the worst plan ever.
Boromir, a noble man of Gondor, who has been preparing to steward over his city and protect his people for his entire life points out that the only logical answer is to “Give Gondor the weapon of the enemy. Let us use it against him!” and in many senses, he is absolutely right. It does seem far more logical to give one of the strongest kingdoms of all Middle Earth the ring, and let them use it’s power to fight back against the darkness that threatens them. For there are definitely some men in that realm who would be strong and valiant, and possibly able to use the ring for long enough to make a dent in Sauron’s forces before the ring corrupted them entirely. It certainly seems more logical than attempting to slip through the thousands of guards in one of the most inhospitable lands in the world anyway.
However, the fact that this plan makes so much sense is exactly why it would never work. Sauron is a ridiculously intelligent battle strategist from his years working under the previous dark lord Morgoth, and as such his cunning is paralleled by none. He would see a plan like this coming from a mile away, and be able to reclaim the ring as soon as it had entered the world of men, whether by using his Ringwraiths on their flying fell beats, or by sending in an entire battalion of orcs doesn’t matter. The whole point of Frodo and Sam trying to slip into Mount Doom undetected and destroy the ring is because this is the only plan that Sauron would never see coming.
Gandalf explains it thus: “Let folly be our cloak, a veil before the eyes of the Enemy! For he is very wise, and weighs all things to a nicety in the scales of his malice. But the only measure that he knows is desire, desire for power, and so he judges all hearts. Into his heart the thought will not enter that any will refuse it, that having the Ring we may seek to destroy it.” Sauron’s sole drive and purpose for existence are to dominate and claim total power over all of the free people of Middle Earth, and so he cannot conceive or fathom that someone in possession of the ring would choose to do anything else with it. In this way, the fellowship are able to exploit one of his only weaknesses, and he doesn’t realize the true intention of the companions until it is too late to do anything about it.
So, as unlikely as it seems, Frodo and Sam truly were the only people who could have been able to complete the quest, firstly because they are hobbits who are generally incorruptible by nature and prove remarkably resilient to the rings enticement, and secondly because they were ‘insignificant’ enough creatures that Sauron never would have even thought of them being the ones to defeat him by destroying his precious source of power.
All of this is, of course, is accomplished thanks to the combined efforts of the fellowship, including Aragorn who fights valiantly to protect them, Merry and Pippin who play fundamental parts in taking out the threat from Isengard, and most importantly Gandalf, who is wise enough to know the mind of his enemy, and enlightened enough to orchestrate how to work around his blind spot.