Increase in value of short call position?

So I read in the curriculum that if you are long a stock, then you can hedge your position by using short calls(assuming you are delta hedging properly)

My problem is that I thought that when you take a short call position, you sell it to someone at a fixed premium at start. I just dont seem to understand how it can hedge you against losses more than the initial fixed premium.

You are correct.

The text is just outlining specifc one and two period examples that allow you to create an arbitrage free hedge ratio; it’s relative to very specfic and known price movements, not all possible outcomes.