why are leg extensions hard on the knee joint?

To understand why this is, it is helpful to understand the concept of shear. Shear in this case just refers to a horizontal force on the joint. Imagine two cans stacked on top of one another, and imagine that a piece of masking tape joins them. Then, imagine what happens if you hold the top can still while you push the bottom can to one side. Eventually that tape will snap. This is a simplistic description of what happens to the knee joint in a leg extension.

Here is a simple diagram that attempts to explain the difference between the squat and the leg extension. The black lines represent the thigh bone, shin bones, and knee joint (black circle). In a squat, as shown in the figure on the left, your feet are on the ground (hopefully), and the force of the load is transmitted downwards, along the length of the bones. In a leg extension machine, there is a pad against the front of your shin or ankle, and you press against it to move the weight. The foot swings upward in an arc. Thus, as you can see in the figure on the right, the pressure is coming across the shin bones, not along their length. This creates the problem in the knee joint as the shin is pressed backwards.

Leg extensions do have their place, usually in rehab. If the leg extension machine is used, it is wise to use a smaller range of motion, perhaps the top third of the movement (from slightly bent to fully straight leg), and light weight.