life empty of attachment is actually the opposite of true independence
~Steve van Bockern
It is very painful to see your child suffering from separation anxiety. Some children cry every time mom or dad leaves. This can go on for many years, making the parents feel like their poor child is being repeatedly traumatized, or that they have done something wrong to make him feel so insecure. But this is not usually the case. It is more likely that the child has a very secure attachment to parents and caregivers (this is why he does not want them to go), but that he has developed the bad habit of reacting to a situation in anticipation of an evil that never actually comes. After all, he survives the separation. He is not abandoned. Mom and dad return. Every time. Moreover, the daycare worker or teacher reassures you the tears last about 5 minutes at most.
So what is going on exactly? Why does he keep reacting this way?
Your child is facing into the fear of being alone. It is not so much that he is still emotionally dependent on you (on the contrary, children only ever feel this anxiety once they have acquired some measure of autonomy), but that he has become exquisitely aware of his own separateness, his existential solitude so to speak. This is all the more pronounced in a shy child for whom the distinction between himself and the world is felt more acutely.
There is nothing you can do to alter the reality of what he experiences, so it is no good trying to persuade him there is nothing to be afraid of. For him, there is. Never sneak away either, as that really is abandonment and will simply breed mistrust and insecurity. Instead, for every new separation, make a reasonable plan, a departure routine, and stick to it. Be loving but firm. And encourage your child. Tell him how proud you are because you know it is so hard it is for him and he is so brave. Remind him that he has survived the fear before and will survive it again. Before and after the separation, emphasize your child's courage. Help your child feel and celebrate this. Do this also when your child takes the initiative in other situations that he finds challenging, like letting go of the side of the pool for a bit when he is learning to swim. But never push a child or throw him into unpredictable situations over which he has no control. This will simply overwhelm him.
Your child may always be an anxious or timid child. But by anticipating and facing into fear, again and again, and by enduring and surviving it, your child will build courage. Courage is not fearlessness; it is endurance in the face of fear.
Finally, be proud of your sensitive child, who is feeling the raw emotions that make him a human being. And be proud of yourself as parents that have raised a child that can still feel this vulnerability.