In the beginning, most students want to pull or push their practice partner to make a technique "work." The brain assumes, after watching sensei demonstrate, that you must force uke (attacker) to move in a certain direction and to do that you must pull or push them. Seems logical, right? It's what the mind thinks it sees. However, in aikido, that is having a "fighting mind." It usually ends with the stronger person "winning." If you're the defender, it's not the outcome you desire.
A concept that works very well, but can be difficult to grasp at first is "move you, not them." When someone tightly grabs your wrist, your mind often goes to the contact point. From there, you try to move, but it's difficult. So, you try harder, add more strength and nothing happens. You're stuck. But if you don't think about the grab, you'll find that you can move much more easily. Just move you, not them. Tohei Sensei once said, "Do not move from where you're grabbed." If your mind is not stuck on the grab, it is free to move to a part of the body that can move. In tune with that advice, if you just think you're moving your arm and not theirs, the arm can move freely.
For example, have someone stand behind you and tightly grab your wrists. Now, try to touch your nose with either hand. If you think about how tightly you're being held, you can barely move. Now, imagine that your nose is itchy and scratch it as you normally would. Give no thought to how the hand gets to the nose. Just do it. Huge difference. Apply this principle in your techniques, especially when working with larger, stronger partners on the mat.
My thanks to Kurt Fowler Sensei of the Arizona Ki Society, and his more than 50 years of training, for helping us better understand this concept.