Its hull would simply not hold together. The same reason you don't see wooden skyscrappers. Wood has several disadvantages that each independently put an upper limit on the wooden hulls:
1) Wood is bendy. The longer the hull is, the more it will potentially. Sideways would be bad enough, but in rough sea conditions, consider a ship hull a kind of a bridge, potentially resting its ends on two wave crests.
Hogging is a problem for steel hulls as well, but it is much more pronounced in wooden ones.
2) Wood is made from trees. There is an upper limit of how long a wooden beam can be due to this simple fact. In contrast, a metal beam can be as long as your needs dictate it.
3) Wood is organic. This means rot and woodworm creating structural weaknesses in random places of the hull, which serves to exacerbate the first two problems. Before you bring up rust, rust is much more predictable as to where it occurs and can be more easily counteracted.
Lastly, though I will not list this as 4) due to it not being wood's fault, since mid-XIX century a metal hull would also simply be cheaper to build than a wooden one, in addition to all of the above. The largest sailing ships all had iron/steel hulls:
https://en.wikipedia.org/wiki/Iron-hulled_sailing_ship
https://en.wikipedia.org/wiki/STS_Sedov (currently the largest sailing ship in service)
