You should never try to make your backswing higher. I totally disagree with your coach. That will throw off your timing and make you muscle the ball. The weight of your ball should carry your arm as far as it naturally goes. If you want to lengthen your backswing slightly, you can hold the ball higher in your starting position, and the ball will naturally gain more speed. This will carry your arm higher in the backswing.
I've never seen you bowl, so I won't completely rule out that your coach had a legitimate reason for telling you this. But it's unlikely.
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