Here is the BIG reason.......WEIGHT.
One of the main reasons.........COST!
Sure, you'll gain some weight by using real wood, but think how much nicer it will make your trailer.
Stability wise, plywood removes the need to worry about this, but if you use well-seasoned wood and finish it properly, you shouldn't have too many problems.
Here are some pictures from
http://www.airstream-trailers.com
This guy has used red oak for the cabinets.
I am thinking of replacing the cabinets in my 1974 31ft Sovereign with real wood, but it won't be red oak. Maybe QS white oak or black walnut as I have a ton of this out in the woodshop!