With today's technology and available materials, why do boat builders still
use wood in the construction of their boats?

You get different characteristics depending on the material you select. There
is no perfect, flawless, material.

It's also tough to say "wood boat" and imply sort of a one-size-fits-all
concept.
Are we talking plywood, either sheathed or stitch and glue? Traditional plank
on frame? Cold molded? Even wood boat fans will argue bitterly about the
competing merits of various wood boat technologies.

Among the reasons people choose for wooden boats:

Quieter, warmer, hull. A more "solid" sensation.

Easier for many do-it-yourselfers to build, or assist in building.

Fewer environmental concerns with construction, use, and eventual disposal (the
initial harvest of trees notwithstanding).

When a boat is a one-off custom build, it is often less expensive to use wood
than to go through the process of creating a mold for a FRP hull.

As far as wood "rotting" when it is exposed to water, it's not as simple as
that. Sal****er actually preserves wood. Freshwater, (including rainwater)
promotes
the fungi that consume wood. Properly cared for, stored under cover, a wooden
boat can last for decades before major structural repairs are required.

Finally, a wooden boat is very repairable.
When a hull fails on a glass boat, it's likely due to a condition that effects
huge areas of the vessel. Wood boat owners aren't surprised to discover they
need to replace one or two planks during a routine haulout of an older wooden
boat- and do so without a lot of drama or catastrophic expense.

After a few decades, most wood boats will need to be "refastened", with new
screws installed to hold the planks to the frames.
This is a labor intensive job that doesn't require advanced journeyman level
skills, and many wood boat owners put aside a number of weekends to accomplish
the task without hiring help.

Wood boats are renewable. Sort of like the story of George Washington's axe. It
seems that somebody found the axe that Washington used to chop down the cherry
tree.....the handle had been replaced seven times over the years and it was on
its third blade, but by golly it was still the same axe. :-)