Maybe "diminish" is the wrong word... what I meant was, Frodo seems to keep wanting to think of himself as the lonely, tragic hero... while his friends keep reminding him that he's just a silly hobbit. I'd have to research it more, but I think it's when Frodo starts thinking too much of himself that he gets in trouble, too. Maybe JRRT was trying to reinforce the idea that *this* crisis didn't need a First Age Hero to resolve it... it needed an ordinary person to rise above himself.
Sometimes I'm not sure if I'm making any sense at all. :)