Try this. Deliberately pull up on the rear pedal while deliberately not pushing down on the front pedal. It will feel strange but do it. You'll see that you can generate some power for a fairly short time before the unusual effort tires out your legs, mostly hamstrings. Maybe 10 or 20 pedal strokes. Then go back to regular pedaling. In a few minutes, switch to pulling up again. Repeat.

Now try something more. In a pretty high gear and low cadence, try pushing with one leg while pulling with the other. Again it will feel strange, and it may take some time before you can develop the coordination. Usually I push my butt back in the saddle. As you do this, the practice at pulling up will be useful.

What is the practical use of this? First, on long rides when your legs are getting really tired, you can give them short breaks by switching to pulling up for 10 or 20 revolutions. Even those little rests help. Second, when you need extra power but don't want to stand up or shift, you can get some extra power for a short burst, by doing the push + pull. Usually this is handy on short grades.

I've never been able to continue pulling up for more than a short time - a few minutes at most. Possibly if you trained it, you could develop more endurance at pulling up. But maybe the training time would be better spent on the pushing down muscles.