I know the current Green Lantern Corps has a weakness to the color yellow, but this has been recently explained by Parallax and that the yellow element is the exact opposite of the green element (fear weakens will). However Alan Scott uses a different ring based in magic which follows different rules. It's been known that his ring doesn't work on wood or plant material, but I can't find any explanation of why.
I did research on Wikipedia which stated that his ring didn't work on wood, and gave a minor explanation as to why:
His ring could protect him against any object made of metal, but would not protect him against any wood or plant based objects. This was said to be because the green flame was an incarnation of the strength of "green, growing things".
However this explanation doesn't appear to be backed by any evidence, and it doesn't really explain the why it wouldn't work.
Another quote from Wikipedia of his ring not working on Wood/Plant material:
Alan's ring cannot affect anything made of wood or plant matter. He can conjure a green shield to block bullets, but a wooden club will pass right through it effortlessly. Solomon Grundy, a zombie whose body is partially made from swamp matter, is highly resistant to Alan's powers.