Dependency of an option price on time till expiry

I am trying to seek satisfaction when it comes to understanding why the price of an option is dependent on the time until expiry.

I have read that the longer till expiration, the more time available for movement in the underlying stock price, and more chance of being on the desirable side of the strike price (assuming positive drift), so this should mean that the option price is higher than when we have shorter times till expiration.

But if the drift was a larger positive, this should mean that the price of the option is greater as we have even more chance now of landing in the money. But this isn't true since the drift does not affect the option price, telling me that the reasoning above isn't quite right.

Could someone please shed some light on how to understand how the time till expiration affects the option price.