In all seriousness, find another mechanic if he’s that easily baffled. In order for anyone here to help you out, you’ll need to provide a lot more details of what going on when this happens. Before going any further I’d do a basic tune up. Fuel filter, spark plugs, oil change, air filter. Then I’d clean the mass airflow sensor and throttle body. There’s plenty of how-tos explaining the last two procedures. If the hesitation is still there after that, it’s going to take some digging to figure it out.

 

what year? what engine? basic info.

If it's a later car, any chance you're leaving TC on and getting some wheelspin? It won't always light the light when Advancetrak or Traction Control intervene.