This is, of course, one of the most hotly argued topics in the modeling world. To my notion there's no definitive answer - except my favorite answer to most modeling questions: to each his/her own.
Surely the biggest reason for the popularity of wood for models is obvious: wood's been around longer. People were building ship models out of wood for (literally) thousands of years before anybody built models of anything out of plastic. People whose knowledge of model building consists of having seen a few models in a museum naturally take it for granted that ship models are "supposed" to be made out of wood.
I refuse to categorize one material generally as "better" than another. Anybody who's seen one of the great (wood) "board room" models from the seventeenth or eighteenth century surely has been blown away. And the detail on some of the plastic and resin kits available today certainly blows me away. I've made the following point before, and I'll stand by it: as a practical matter the mold making and casting processes today are capable of producing far finer detail than any modeler can achieve by hand. (If you don't believe it, take a close look at an LP record.)
And I think anybody who's worked much with wood will confirm that it produces a type of satisfaction that's different (notice I didn't say "greater") than a plastic kit can give. But the same can be said about working from scratch in styrene - or, for that matter, metal. (I've never scratchbuilt a working steam locomotive, but I imagine the guy who does gets at least as much of a high out of watching it chug around the track as I got when I finished my scratchbuilt Hancock.)
What bother me are the people who do contend that "real ship models are made of wood, and plastic ones are fakes." Those people just don't know much about plastic models. I'm particularly galled by the people who build those awful HECEPOB (Hideously Expensive Continental European Plank-On-Bulkhead) kits, and think the grossly inaccurate finished products are "better" than a genuine scale model that's made out of plastic. I once dropped out of a ship modeling web discussion group because it literally banned plastic models. That strikes me as a great way to shoot oneself in the foot.
My own personal approach is to use whatever material I think is best for the particular job at hand. That little Hancock model contains basswood, boxwood, pearwood, holly, styrene, britannia metal, brass, steel, silk, silkspan tissue, silver/tin solder, nichrome wire, copper wire, and probably a dozen or so other substances that I can't think of - plus walnut, plywood, velvet, and plexiglas for the case. My personal list of no-no's consists of two materials: lead (because it's one of the least stable substances on earth) and balsa wood (because I hate it).
Personally, I've always had a little trouble with the idea of building a model of a modern, iron or steel ship out of the wood. It just doesn't seem quite logical. But we've all seen magnificent wood models of battleships, liners, and destroyers. Please don't try to tell me that wood is the "only legitimate" material for a modern steel hull, though.
It's a great hobby - and, to my notion, more than that: some ship models rise to the level of art. But I don't think modeling in general benefits from trying to impose universal value judgments or rules on it. I repeat - to each his/her own.