Sometimes, the quote feature doesn't work as intended. I can't remember which posts it happened to, but if one looks around it shouldn't be too hard to find...
It should look like this
[qutoe]Not this![/qutoe]
(quote intentionally misspelled to demonstrate problem)
This is pretty simple. The fact of the matter being you need a proper quote tag at the end of a quote in order for the forum to register it as an actual quote.
All closing quote tags need a "/" in order to successfully designate the selected text.
It can also happen if a person inserts quote tags manually and forgets to depress the quote button... the forum automatically adds a "[/quote]" to the bottom of all posts if it's only been pressed once.
Beside missquoting quote text, perhaps one reason why the quote does not work is that the poster accidentally ticked the "Disable BBCode in this post" box.