Oz,
That's a valid question. The answer isn't so much in what the rudder does, but what it doesn't do. Specifically, it doesn't withstand loads for which it wasn't designed.
In airplanes, we do nearly everything based on speeds. We lower flaps at certain speeds, raise them at certain speeds, bring the nose off the ground at certain speeds, penetrate turbulence at certain speeds, land at certain speeds. It's all about the airspeed.
There's a speed known as "maneuvering speed," at which pilots are taught from their early days of flying, that a particular control can be given a full deflection without harming the airplane. That is, if one gives full left aileron, for example one should stall the control surface or the flying surface before one can build up enough force of loading to damage the airplane. If one is at or below that speed, the theory goes, one can't really hurt the airplane. The problem is, this is an extreme oversimplification, and therefore a fallacy when applied to many operating conditions.
The crew of flight 587 were taught the same as every other crew had been, and were not aware that the certification standards for making a full control deflection were for ONE control deflection. What they did was use the rudder to counter some wake turbulence through which they flew...something that's commonly done in a light airplane, but not so much in a big airplane. Specifically, they performed a control reversal...full rudder one way, then full rudder the other way.
The easiest way to imagine this is getting punched in the stomach. Get punched in the stomach, you double over. That's the first control deflection. However, if while you're doubling over, someone were to punch you in the face, you get hit not only with the force of someone's fist in the face, but he force of you bending into it...a double whammy, if you will.
Same for the airplane. Deflecting the rudder fully one way applies a bending and torsional force on the vertical stabilizer; the stresses it's experiencing are high, and are in effect, bending one way. Suddenly reversing it not only applies forces in the opposite direction, but increases them. Simply put, the airplane was designed for one full rudder deflection in one direction, but not a second one in the opposite direction. The truth is, it is possible to break an airplane at lower speeds than many previously believed.
Since that time, there has gone on considerable informing of the industry, educating, and passing along of information that should have been made clear before. This doesn't help the crew and passengers of Flight 587, of course. An additional wrinkle in the issue is that Airbus aircraft are supposed to be written with "laws" in their computer logic that prevent this sort of thing. In that case, it wasnt' applicable, and shouldn't have been a problem...it was an unforseen combination of control inputs that broke the airplane in flight.
I used to fly a large four engine WWII airplane on wildland fires. We threw it around the sky like a supercub (little single engine general aviation airplane). That included constant full deflection control inputs, full slips down canyons, etc. That airplane has a very tall, big vertical stabilizer. That means very large loads are put on the vertical stabilizer. What we began to find during deep maintenance checks was that the attach brackets and bolts for the vertical stabilizer (the tail) were cracking or breaking. I quit doing full slips in the airplane.
I'm sure the big question in your mind is how this applies to you. You shouldn't be worried. For a number of reasons, there's no reason this should ever happen again. I've flown a couple of airplanes which broke up in flight, losing their wings...not when I was flying them, obviously. In one of those airplanes, a wing did break when I was flying it. Those were flown on fires, and were subject to considerable stresses that airline aircraft are not. They were also much older than any airline aircraft, with a lot more exposure to a violent environment. You won't see this sort of damage, stress, or wear in an airliner.
Last week I encountered severe turbulence during a flight over the ocean. When we arrived at our destination, we were greeted in the cockpit by mechanics who took our report, and immediately went to work taking care of any necessary inspections. This takes place after each landing in an airliner. The aircraft tend to be newer; new design materials, newer engineering, newer powerplants...and most importantly...what's designed today is often based on learning made from errors of the past. Aviation has come a long way. The Airbus crash was a tragedy, as is every loss. It's important to understand that it wasn't a design flaw, but an operational error...not one remotely likely to be repeated again.
I've been flying airplanes, large and small, into conditions of severe to extreme turbulence for many years...conditions that are very, very rarely, if ever encountered in airline flying...without damaging an airplane so far. I've flown aircraft intentionally during research into thunderstorms that broke headsets and even my personal computer on board in turbulence, but through which the airplane flew without incident (thunderstorms are dangerous places, and I don't advocate ever going in one, incidentally...and airline operations avoid them like the plague).
I suppose what I'm really saying is that you have a very valid question, but no reason to worry.