Stimming is a term used with Autism to describe repetitive, self stimulatory behavior. The behavior can vary in many ways: hand flapping, spinning wheels, pacing back and forth – it’s different for everyone. I had 2 parents approach me with their concerns that a professional, either a Doctor or a BCBA, told them to be concerned about their child’s stimming.
Do these professionals not know what Autism is? It’s a neurological disorder, which means they process information differently than you & I. Leave them alone! Stimming can occur for numerous reasons: anxiety, happiness, over stimulation in the environment. Just because it’s not how YOU show emotions, doesn’t mean it’s wrong.
Stimming is a form of energy, it has to come out. If you try to stop someone from stimming, do you know what’s going to happen? The behavior is going to change to a new form of stimming!! It’s going to happen, whether in front of your face or behind your back.
There are professionals out there that can’t think for themselves and say/do what they have been taught by the University. You, as a parent, are allowed to get a second opinion. You don’t have to do what they tell you. Do what feels comfortable to you, after all, they are YOUR child.
My recommendations: Accept your child the way they are & love them unconditionally. They are already perfect, for they too were made in God’s image. Just because they stim, doesn’t mean they can’t learn. Everything is going to be fine. We all have our quirks anyways.
Therapy Ever After 
My 5-year old son wipes his saliva on anything he likes. I joke about it saying he is “blessing” the things he loves. But I do worry when he will outgrow this. You’re right about how kids move on to other forms of stimming if you stop them. My son used to be crazy about straws and flicking one until he got tired of it and got another one. I hope my child can find a form of stimming that will not be too obvious.