Dwarves cut down 'living' trees. The Elves cut down and use 'dead' wood. So instead of killing a living tree (with which they are 'friends'), they are simply making use of something that is already dead. Elves
HATE it when trees die.
Pretty much the same reason as to why they eat all of their kills after battle (read 'fallen enemies'). I guess they try not to waste resources, while trying to respect all life, not just animal.
The main reason they won't accept your wooden goods for trade is that they can't make sure you got your wood from dead trees. They seem to feel that Dwarves don't care for nature and really don't care if they kill trees.
To put it in perspective, think of DF wood like Real World diamonds. There are 2 kinds of diamonds, 'Clean Diamonds' and 'Blood Diamonds'. You would only want to buy 'Clean Diamonds' because of the torture/slavery/conflict/bad stuff associated with 'Blood Diamonds'. Elves want 'Already Dead Wood' not 'Made Dead Wood'. Of course you can get certification that the diamonds you buy aren't 'Blood Diamonds' but the Elves can't get the same sort of thing for wood.
That is why they want you to stop cutting down trees and why Elves don't want your wooden goods.
Pansies.