black scholes - Why does a higher stock value imply a higher call option value

This may seem like a very dumb question, but if the underlying stock price is greater, then why should a call option be worth more.

My reasoning is that, if the option price is not affected by the drift of the return from our stock, then this implies we are not bothered whether the stock price increases or decreases on average in the future, due to the hedging strategy we have set up in the derivation of the Black Scholes equation.

Now people will say that a higher stock price means we have more chance of being on the desirable side of the strike price, implying a higher option value, but from the above, we are assuming we do not care on whether the option has more chance of lying above or below the strike price. So surely then a higher underlying stock value shouldn't affect the call option value.