A tripod can be unstable by:

Having cheap leg fasteners / too heavy a load for the legs

• My first tripod ever was a hand-me-down Velbon that had seen some abuse. Even sporting just a 20D and 70-200 f/4 (~3.2lbs) if left alone, the legs would begin to collapse. Slowly, sure, but enough to not want to walk away or be able to do a long exposure.

Poor Quality Feet

• A decent, sticky rubber is most often used, as it will work well on dirt, rock, decently in sand (might sink a bit), cement, etc. Cheap feet (or even old feet) will be less sticky, negating these benefits. And really cheap feet may even expose a screw head or some metal - causing real slipping issues when used on hard surfaces.

Height to Base ratio

• You’ll notice that you have a lot of stability when the distance between the legs is greater than the height of the tripod. As you increase the height in comparison to the distance between the legs, you lose stability.
• This is doubly true when extending the center column or when photographing in high wind.
• In public places, someone could knock into your tripod. Whether or not you have to dive for it is dependent on this stability.

Where is the Center of Mass?

• Top heavy things in general are less stable and are easier to get moving, whether by wind, vibration, or some other force.
• Actions can be taken to counter-act a heavy camera on a (especially) light tripod, such as attaching weights to the center column or using something like a sandbag over the legs.

Vibrations

• Different materials handle vibrations differently. That same Velbon aluminum tripod vibrated enough to ruin photos at 400mm if a car drove by within 20 yards. It also vibrated for every small gust of wind.
• Generally speaking, the more material there is, the more vibrations will be dampened. Thick aluminum will work better than thin. Different materials also behave differently – carbon fiber, steel, aluminum, etc.

Head Design

• Some cheaper tripods come with built-in heads, as it negates the buyer from having to find one and creates an all-in-one ticket item. These can suffer the same fate as the cheap legs – the build quality can be such that, even tightened down, they still move over time or if influenced by wind/vibration.

Assuming that your chosen tripod could withstand the weight of your equipment without collapsing, and if it were tested in a vacuum, I would expect it to be on par with every other tripod of similar or better build quality.

But the real world has wind. It has people moving about. You may not notice that something as benign as a small gust could shake your shot during a moderately slow exposure – but the problems will exacerbate as your exposure lengthens.

The sturdiest of all tripods will withstand a heavy load, wind, and vibration. It’ll also weigh an absolute ton. As you look into models that shave weight but still maintain overall sturdiness, you’ll notice that the price starts to go up. Finding the right one for you means weighing your use case against price, carry-ability, pack-ability, load bearing, stability in wind, and stability with vibrations. Hence, the many differing designs utilizing differing materials and head types, at all different qualities.