doghouse:
ok, so we are taught to grip the bc/harness with our left hand, and proffer the octo (or primary) with the right hand. Once the OOA person accepts the octo you right hand is free you get settled and start your ascent. You now have to reach across with your right and to take your inflator hose and control your ascent.
Why not, grab the person with your right hand, pass off the octo with the left (reach across body 1x, then the receiver is locked to the side your octo is on, and you have access to the shoulder dump on their bc and have your left hand free to control the ascent. Why is this wrong? Other than the fact that it is not taught that way.
You may want to check back with your instructor to be sure that is how he/she wants it to be done. Whatever your particular instructor is teaching, then that is what you should do for the practical exercises.
At some point in the drill, you need your left hand free so that you can operate your BC or wing deflator hose. Therefore this drill is normally taught in a manner so that your left hand is always free, rather than using it to hold onto your donee-buddy's shoulder strap.
The first thing you need to do, however, before you grab anything, is to extend your 2nd stage, either primary or octo, depending on how you are configured, to your buddy. That is what your buddy needs the quickest, so that is what you need to do, the quickest. No grabbing anything yet.
The risk in air sharing is always that you and your donee-buddy will drift apart. That is why you would normally hold onto your buddy's right shoulder strap with your own right hand. Remember that his/her right should strap is going to be to your left as you face each other.
Technical divers with 7 ft hoses normally do not hold onto each other during air sharing. It is assumed that they have sufficient buoyancy control that they will not drift apart. But ordinary recreational divers are taught to hold onto each other during air sharing.
Ask your current instructor how this is to be done in the class. Then come back here again, after you are certified, and ask us how we each do it. You will get a lot of different answers.
I scuba with a DPV (scooter), therefore I always need a long hose about 7 ft for air/nitrox/trimix sharing.