Why Does My Beardie Wave Their Arm?
When your bearded dragon spots a larger beardie, large animal, or an object that the dragon simply mistakes for another animal, it may stand on three legs, raise the remaining leg, start waving it in circles, switch arms or use the same arm again to wave. In this way, your lizard signals submission. Because your dragon is smaller, you'll see this behavior more often in young beardies than in mature adults that are larger.
Bearded dragons may also display this behavior when they want to acknowledge the presence of another bearded dragon or something else that they perceive may be a potential threat. Doing this is their way of alerting to whatever they can see that the dragon is there, not to be surprised if they see the dragon and that the dragon is no threat to them and won't attack, so they would appreciate this to be reciprocated.
Although this is usually a gesture of submission if your lizard pet raises its front arm and waves at you, you can interpret this as a friendly gesture, as your beardie is saying 'Hi' to you. You can wave back to your dragon if you wish to; there is no harm in it.