Here is my YouTube video in which I demonstrate the close-up footwork of a degage:
You're probably doing it wrong. That's okay. Lots of people do it wrong. Here are 3 ways along with their corrections:
1. You don't push the foot against the floor. Instead you lift it and place it on the return, heel first. This makes the movement clunky and stiff.
Correction: press the foot into the floor to initiate the movement, then glide the heel-ball-toe off the floor until the foot points enough to lift it from the floor.
2. You wait too long to touch the floor on the return. When you bring the foot back to the position, you wait until the ball of the foot (or worse, the heel) is about to hit the floor, then you close the position.
Correction: on the return, hit the toes on the floor as far away from you as possible, and then pull in the ball of the foot and finally the heel at the last second. The visual image of the toes melting into the floor can help. This will insure the longest line possible, especially when translated to the center for glissade, etc.
3. Your degage is short, moving from the knee down. It's then very hard to do fast degages without looking short and "choppy."
Correction: perform the movement with the entire leg, from the top of the thigh all the way down to the foot. This will make the line longer and will allow you to do very fast degages because it gives you plenty of room under your hips.