Consider the following scenarios.
Alice sends me 1 BTC, I send Bob 1 BTC.
In this case, I have no Unspent Transactions.
Alice sends me 1 BTC, I keep it with myself
In this case, 1 BTC is unspent transaction output for me
Alice sends me 1 BTC, I want to send 0.25 BTC to Bob, and keep 0.75 with myself
In this case, I have to create two transactions
I send 0.25 BTC to Bob
and
I send 0.75 BTC to myself (using a change address).
Modern Bitcoin wallets do this automatically
The keypoint to note there that INPUT is always equal to OUTPUT (Spent or Unspent).
You cannot arbitrarily split a bitcoin and keep a part of it with you.
