Teachers normally highlight the risks of injuries for particular dance moves, but injuries still happen. Dancers are often interdependent, with one partner taking part of the other's weight or balance, and with spins meaning that partners momentarily lose sight of each other, resulting in a risk of collision. On a crowded dance floor there's also the risk of collision with other dancers, or with columns, furniture and walls.
In a typical dance couple there's also an imbalance of strength. The leader (usually male) is normally significantly stronger than the follower (usually female). Given that the leader is (at best) guiding the follower, and (at worst) forcing the follower, there are several ways that the leader can hurt the follower through poor technique.
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I've been hurt a few times over the years. In some cases the injuries were a attributable to my partner, and in other cases they were due to my poor technique. Some examples are:
This generally happens when I lead a sway or similar, and my partner steps back with her right foot and her heel lands on my toe. Not a problem if she's wearing flat shoes, or keeps her weight forward; otherwise it can hurt. Last year I had three instances in a period of a month or so, and my toenail is only now returning to normal. But I consider this injury to be my fault: I put my partner into that position, and so it was my responsibility to get my foot out of the way.
It's uncomfortable dancing with a partner who has protruding rings, and sometimes I have suggested that my partner to take off a particularly large ring in future. Generally the large ring is on the left hand, so I can avoid it. But the only time a partner has drawn my blood was a total fluke, and in that case it was with her fingernail.
I'm thankful that I wear glasses, because they protect my eyes when my partner's spinning. I've been whipped in the face many times - but it's rarely a problem. If my partner's hair is in a ponytail it can hurt more than if it's loose. Again, since I'm the one who puts my partner into a spin, I take responsibility for getting out of the way.
I had a fluke injury when I spun my partner in for an Astaire, and she left her arms wide. In that case she chopped me in the throat. A fraction lower, and she would have struck my collarbone, which wouldn't have hurt. But in this case it did hurt, and if it had been a little harder, it would have been a very serious injury.
I had one inexperienced partner hold on to my middle finger too tightly as I was spinning her or returning her (I can't recall which). She wrenched the finger, damaging ligaments. I will never regain my original strength in that finger.
I've had back strain and knee injuries in class, as a result of inadequate technique. This shows up most with heavier partners. It's one of the hazards of doing more advanced moves, and injuries are more likely when learning. But it does reinforce the importance of the lead keeping knees over toes, and a straight back.
In freestyle I've avoided injuries when my partner has led herself into dips, thanks largely to quick reactions. But that's the most common cause of back injuries for leads.
Common events that don't hurt (or only hurt briefly): my partner standing on my toes with her toes; my partner striking my body with hand, arm or elbow. Generally my partner is lighter than me, and her accidental contacts don't contain enough momentum to hurt much.