Why do outputs need to be spent entirely?

Why do outputs need to be spent entirely?

I understand what change is and how it works (and it's analogous to physical money change), but what I don't understand is why this is needed in the first place.

Given that this is all computer based, I thought that money could be sent just by saying “I will give you 0.5 BTC” and verifying that your addresses in fact contain more than 0.5 BTC, and then substracting the spent amount.

So, my question is, why does the protocol define that outputs must be spent entirely? Where's the benefit of doing that instead of just sending the fraction that is needed?

https://ift.tt/2rb9Bry