Aragorn: And you’ve no duty to your own kingdom at the moment? You know, what with being next but one after the heir?
Éowyn: Yeah, but…
Aragorn: But?
Éowyn: But I don’t wanna do it!
Aragorn: Sorry, but I can’t take you. You’ve no business along with me anyway.
Éowyn: But I love you!
Aragorn: you’ve only known me five minutes, and I’m engaged already. This is not going to end well Even more sorry, but no.
But it’s worth noting that Théoden refused to allow Merry to ride with the Rohirrim for precisely this reason: he would just be in the way. After the fall of Isengard, Gandalf took Pippin with him when he rode to Minas Tirith for the sole purpose of getting Pippin out of the way. And for that matter, at the formation of the Fellowship, Elrond spoke strongly against Merry and Pippin being included in the first place.
And as Malacandra pointed out, Éowyn had a duty to her people that constrained her from riding with Aragorn, even if he had been willing to take her. Sam, Merry, and Pippin had no such tethers, so they were able to insinuate themselves into the Fellowship through sheer force of whining.
Hear, hear! Perfect schmerfect; no writer (or work) is without flaws, notwithstanding the fact that no force in the universe can save a timeless masterpiece from the gentle but captious scrutinies of its most devoted fans. I’m only too happy to join a toast to the brilliance of Professor Tolkien’s literary achievement.
Strangely enough, I was just reading about the Icelandic Sagas that chronicle the Viking settlement of North America. A woman, some relation of Leif Erikson I think, led the final voyage to Newfoundland. When they were attacked by the natives, she advanced toward them, exposed her left breast, and slapped it with the broad side of her sword. This display scared the hell out of the attackers and they fled from her.
Giving more thought to Tom Bombadi, I understand the character’s limitations as they were written but his power over the ring suggests a greater function within the story line. I expected him to carry as much weight as the other main characters and his dominion should have been written to allow a greater role.