Short call in binomial option pricing model
One reason why you might want to do this, and perhaps is the motivation for this example, is that it gives you a simple example for thinking about option pricing.

Under some assumptions, the value of any option can be replicated by continuously trading in the underlying asset. Here, you can think of the $\Delta$ shares that you have as your replicating portfolio, and the amount $\Delta$ is meant to be chosen so that the value of these shares is exactly the value (to you) of the call option you just sold.

You can then price the call option according to how much those $\Delta$ shares cost you. If you chose $\Delta$ appropriately, you break even, and this determines the "market price" for the call option you just sold. This example doesn't give you quite everything you need to calculate that yet, but I imagine whatever you're reading is building up to get you there.