If you think about it, this is somewhat obvious - and yet most don't really think about it when fixing a technique, leading to great difficulties in making these changes. They'll try to fix one part of the technique, but unless they fix both parts at the same time, the technique won't work properly.
Imagine a player with perfect technique. Now imagine changing something so his technique is no longer perfect. He'll likely have to compensate somewhere else in his technique for this change or his shots will no longer hit the table. Similarly, a player with one poor part of his technique will almost always have at least one other poor part to compensate.
For example, let's suppose a player's backswing is too short on a loop. To compensate, the player will likely swing more violently to gain the racket speed, leading to a poorly-controlled jerky stroke. To fix this he has to both extend the backswing while slowing down the acceleration to a smoothly controlled swing.
Or suppose a player hits or loops forehands with his right foot (for righties) too far back. To compensate he'll likely have less waist rotation (since otherwise he'll literally be facing backwards during the backswing, leading to an awkward and less-powerful stroke. To fix the problem he has to both bring the right foot a bit more forward while increasing the waist rotation.
Or suppose the opposite, that the player hits or loops forehand with his right foot slightly forward (i.e. a backhand position) or even with the left foot (for a player who doesn't have a supple waist and/or spend many hours each week training like top players who correctly do this). The player will likely find it difficult to rotate the body properly in the time needed in a rally, and so will tend to stroke with only the upper body and arm, again leading to an awkward and less-powerful stroke. To fix the problem he has to both adjust the foot position and increase the body rotation. (Note how both improper foot positions lead to difficulties with using the lower body and proper body rotation.)
The same is true of a player who plays with his two feet parallel to each other, which makes it harder to rotate the lower body, and so leads again to an awkward and less-powerful stroke. Again, both the foot position and the body rotation need to be adjusted. Telling him to do one without the other won't help.
Or imagine a player who stands too far off the table when forehand looping against backspin, a common problem. He'll have to reach forward too much in his swing, and so to keep his balance will have to pull back with his left side, and so fall backwards slightly, leading to a loss of power and balance. Telling the player not to fall backward won't help unless you also tell him to stand closer to the table. His contact point with the ball may be the same, but it won't be so far in front of him.
Another common problem is the player who lifts his elbow during his forehand drive, leading to the racket angle changing from too open to closed during the stroke, making it hard to control what the angle is right at contact. If you tell him to stop lifting the elbow without also focusing on starting the forward swing with the racket in the proper angle he'll have great difficulties.
Sometimes there are more than two roots to the problem. If a player stands up too straight, this forces all sorts of adjustments to compensate. When the player tries to stay lower with a wider stance and knees more bent (as he should), he'll have to change a number of aspects (for the better) to his stroking technique. But if he doesn't make these changes, his new stance and stroking techniques will be awkward.
There are many more examples like this. What technique problems do you have in your game, and is the root of the problem singular or plural?