I've often thought that Aragorn
could have been quite prideful and arrogant, if not for the fact that he "learned better" rather quickly. Remember how, when he was first told about his lineage, he felt quite puffed-up and self-important about it, until he met Arwen and suddenly felt small again. Somehow, he found a proper perspective about his own importance in the world as a whole. Being human, he will not be perfect, of course, but when compared to some of his contemporaries -- Denethor and Boromir come to mind -- he has a much more balanced sense of both pride and humility.
There's also the question of what Tolkien meant by "humble." Sometimes, I think the definition changes. At times, it refers to modesty and meekness, at other times about a more lowly status. The hobbits might be considered humble not because they lack arrogance and pride, but because they are a younger, less complex, more innocent society. They have had struggles to survive in their past, but they were usually against nature, not against legions of orcs and power-hungry Dark Lords. The cost of widsom all too often is the loss of innocence, which all the Shire lost to some degree when Saruman and his lackeys invaded it, but which Frodo lost more than any other, to the point that he no longer could remain a part of it. He had seen too much, endured too much, faced his own pride, failed, and was humbled -- what John Campbell might have called his heroic "descent into hell," a necessary part of his heroic journey to an eventual personal apotheosis.
Not all of Tolkien's heroes in LotR go through this journey, but at least a few do. Gandalf literally descends into hell with the Balrog, and to death, to achieve a rather literal apotheosis and rebirth by the will of Eru -- a thing which might not have come about if he hadn't willingly sacrificed himself and his own goals to save the quest, the success of which was paramount. Aragorn, prideful and stubborn before the doors of Meduseld, must later choose to take the paths of the dead and risk his own life in order to achieve a greater good which may not lead him to the throne, but is the only hope to keep Gondor alive until Frodo's quest can be achieved. He may arrive in Gondor with his standard flying and wearing the Elendilmir, but after this has the proper effect of putting fear and doubt into the enemy, he is much more humble in his demeanor, refusing to put himself forward as the king he has not yet truly earned the right to be.
I think I'm rambling, now. Sleep first, think about this some more later....