I've seen dowels, dovetails (and other joinery techniques), glue and many more used for joining pieces of wood but metal screws, brad nails and metal, in general, is usually avoided.
Why is this?
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Tradition plays a large role in it, but generally metal fasteners aren’t ideal:
There are plenty of workarounds and alternatives to the issues presented, but wood is plenty strong to join with and the techniques are well established.
A lot of woodworkers enjoy the challenge of building stuff using only wood. There are greater and lesser degrees of this. Some people go so far as to build hinges and latches and locks out of wood, for example, though by tradition, most woodworkers metal hardware for these elements.
To expand on the points Coreyward made in his answer, the traditional techniques are largely what they are because of what was available at the time the traditions were started. Mass produced screws are a relatively recent phenomenon; the Robertson head screw was invented in 1908, and the Phillips head in the early 1930s. The flat head screws available before that were more expensive and harder to use. (source)
Traditional joinery uses tools commonly available in a wood shop for other purposes already. For example, dowels are easy to use and aren't hard to make. Even tricky joinery like dovetails that benefit greatly from a special saw to cut them still only need that one saw that can be used for every dovetail you cut, unlike screws, which would become a material cost. Glue is much cheaper.
But screws aren't universally eschewed. Pocket hole joinery has become more common in recent years. Lots of woodworkers are perfectly happy building designs using pocket holes as the primary joinery method. The wide availability of jigs for making pocket holes from Kreg have made this much more popular (though it is by no means necessary to purchase a jig to make pocket holes; like most jigs in woodworking, you can easily build one yourself). This post may be of interest to you if you want to read more about pocket holes and how to use them.