Because you owed your father money in the end, and the $100 was never yours to take to begin with. The only reason everyone is happy is because you all owed each other that $100. So even though it never increased their income, it settled their debt, thus leaving them content to move on with their life. However, if you put the money back where it was, you not only owed your girlfriend, but your father as well. However....your debt with your father will not be fulfilled unless the debt would have been caused by that $100 not coming back to him in the end.
Reduce the number of people to two, you and your brother. Say you owe your brother $100 and your brother owes you $100. You can either physically pass $100 to each other, or just agree to call it quits. Either way, the end result is the same and a similar argument can be applied to the original question. The actual $100 bill is not physically needed in the debt settlement, as the debt is circular.
Because you all owed $100
With all the borrowing of money you may have well just gave 100 to your brother.
After that you are still out the hundred you gave away.
You lose.
Because you are still out your 100, silly.
