Ben explained, but I'll extend a little, hopefully explaining more why keeping the center column not extended avoids the problem.
A tripod with camera right at the top is a very stable structure, because force on the camera downward results in compressive force on the legs. Assuming a decent tripod, with good clamps, it will resist that force very well. Force directed sideways results in a lifting force on one part, and compression elsewhere. If we put some weight under the tripod, we can keep the downward force dominant, which is ideal, keeping a compression force linear along the legs.
If the center column is extended, resistance to horizontal movement is dependent on the strength of the column. As Ben said, it's like a narrow building. The center column resists bending, but it does so because when you flex the center column, the side you're bending towards compresses, while the side you're bending away from stretches. But those sides are so close together that there's very little mechanical advantage.
It's just like a power pole or telephone pole. The pole itself will resist a bending force, but for real resistance, you see a diagonal guy wire running down to the ground, much like the diagonal leg of a tripod.
As soon as you raise the column of the tripod beyond a couple of inches, it will be the weakest part of your support system. Many people remove it entirely, and put their tripod head directly on the legs, but as long as you understand the limitations, there's no reason to give up the flexibility. Just don't use it, as Colin says, if you're taking a multi-minute exposure.
Cheers,
Rick
I've been using a Benbo Trekker for 20 years and I wouldn't part with it. Sure it's getting heavier as I grow older but it has served me well. With tripods it's trade off between weight, sturdiness, and price. Buy a cheap lightweight one and you get what you buy-a flimsy one that moves in the breeze and falls apart. I prefer quality and I have to put up with the weight for the sake of the images.
Barry
I thought you all might be curious to know what I ended up choosing for my sturdy amateur tripod.
I chose the Manfrotto 190XPROB (which has the horizontal column feature) and the Manfrotto 496RC2 Compact Ball Head. Ultimately, it came down to the price factor. I couldn't go overboard because a college kid needs to eat, too. I think this one will allow room for me to grow (legs hold 5kg and head holds 6kg and my camera and three lenses combined are about 2kg) but isn't extremely heavy or unwieldy.
UPS should be delivering it next Tuesday!
Thanks for the comments and suggestions.