Imagine there is a wheel in-front of your chest, in the same orientation the front wheel of a bike would be if you were riding it, but smaller and up higher.
Then point your index fingers toward each other so that they are both tracing the same wheel. They can each go forward or backward. Most people struggle with making them go opposite directions. To the point that they'll do it once or a half of a time, and then switch directions with one hand and not even realize it. It's fun to teach kids.
You can do it with your whole hand, or arm, or just the fingers, with different size circles, each takes a bit of practice once you get over the initial hurdle.
If I imagine the wheel over my head (as if the wheel axle was vertical), or in front of me but the axle going forwards (wheel is moving left/right), I can do the opposite circles just fine.
But if I imagine the axle going left/right as you describe, it takes extra cognitive effort. If I imagine drawing circles, I can't do it. Instead, I have to think of each axis of movement separately. In my mind, I'm not thinking "Draw circles in the air", but rather, "Move fingers forward and back, while moving arms up and down".
The end result is the same, but what's happening in my mind to get there is totally different.
This was my first time trying to explain it in text without just resorting to making a video. SamBam's reply, and yours pointed out how much different it is in the different orientations. No clue why though.
I normally just ask a group of kids "hey can you do this?" then after I explain that it's different directions, watch them laugh as they try to do it.
Then point your index fingers toward each other so that they are both tracing the same wheel. They can each go forward or backward. Most people struggle with making them go opposite directions. To the point that they'll do it once or a half of a time, and then switch directions with one hand and not even realize it. It's fun to teach kids.
You can do it with your whole hand, or arm, or just the fingers, with different size circles, each takes a bit of practice once you get over the initial hurdle.