Not all targets will stand still and let you shoot them.
When you think about it, competition sets us up for some unrealistic thinking for defensive encounters. The biggest being, when someone is getting shot at, they don't just stand there and take it. So when a moving target is introduced into the competition, it can make taking that target down a whole lot harder.
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In both USPSA and IDPA, there are a number of different kinds of moving and swinging targets. In this video from the U.S. Army Marksmanship Unit, PVT Coley demostrates and talks about some tips on how to shoot several different types.
As you can see, timing is important as well as technique used to engage each target.
Sometimes using the ambush method, where you set your sights and allow the targets to come to you and then shoot, is better then trying to follow the targets and shoot them.
Whichever method is most comfortable and accurate for you is what you should use.