@FSWer I am still not sure what you mean by a spotter. In gymnastics a spotter can do things like grab or move a gymnast who is falling off an apparatus, so that the gymnast falls more safely. Or they can hold a gymnast and push them through a move on the floor or on an apparatus, so the gymnast can learn what the move feels like.
But a skating coach can't do those things. A gymnastics coach is standing on the ground. A skating coach is on skates and is moving on the ice. They're not on a stable surface like a gymnastics coach is. So skating coaches can't do things like grab a skater to stop them from falling when the skater is landing a jump.
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@Clarice says, a skating coach will watch you skate and maybe hold your hand or adjust your body while you do a move. But they can't save you from hurting yourself, like a spotter can in gymnastics.
I'm still also not sure what you mean by a lean in ice dance. Ice dancers are leaning all the time, because they are always skating on an edge, and being able to lean helps them stay on their edges. But it takes a LOT of work and practice to be able to lean as much as an ice dancer does. It looks easy, but it isn't. You have to be a really confident and strong skater, and be able to feel when you are skating on a strong edge. A coach can help you learn all of those things, but you have to learn for yourself how it feels for you when you are doing it right. And that means doing it over and over and over again, and sometimes falling.
A coach can't hold you up when you are skating in a lean. The coach would have to be very close to you to hold you, and you might not be able to lean very far because of that. If you slipped off your edge - which is very easy to do in a lean - it could be very dangerous if the coach tried to catch you. You could both fall quite badly.
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@Yazmeen says, we are not trying to discourage you from your dream. But we want you to be safe. Skating can be really dangerous and it is very easy to get hurt, even when you're doing simple things. To be as safe as you can, you need to have good basic skating skills. You should only try moves that you've discussed with your coach and that your coach thinks you are ready to do, and, at least at first, only do them when your coach is supervising you.