I see this statement time and again. What I understand that an address has its input & output transactions.
Wrong.
So, by deducting output transaction balance from input transactions, what we get is address balance. True, it is a derived parameter, but it is there... is not it ?
There are no "addresses" in raw bitcoin protocol.
There are "outputs" and "output scripts".
The trivial example is escrow output:
You sent some funds to an escrow script of Alice, Bob and Charley. Each two of them (2-of-3) can decide what to do with these funds.
OK, but what is the balance of you, Alice, Bod and Charley after you sent your funds? Who is an owner?
Sorry, I can not explain it in good English.