Aiki can be taken as moving together or dancing. Aikido is referred to as the dancing martial art. In ballroom dancing when the gentleman moves he leads the lady so the she moves exactly with him. It would be extremely rude for the man to walk off and leave the lady by herself. The same is true in Aikido. Every move that Nage makes must move Uke. There is no wasted movement. It is not unusual for a tyro to make a move that leaves Uke standing there. This is very rude and also very deadly for Nage. Leading in Aikido is quite similar to leading in ballroom dancing. The difference is that in Aikido the object is to keep Uke falling out of control the entire time. My understanding is that it is considered a mistake in ballroom dancing if your partner falls.
Sometimes it seems that Aikido gets where it is more like ballroom dancing than martial art. This is not what is meant when Aikido is called the dancing art. It means that we dance with our death.