I was light on a hand, namely six dollars short. I took six chips out of the pot (agreed to by the players) and lost the hand. I gave the winner six dollars cash (representing my short in the hand) and then the player wanted the chips as well. Didn't I just give him $12?
In low-stakes home games it is sometimes allowed, as you point out, for a player to "go light", meaning to borrow money from the pot itself to make a call. This is never allowed in Casinos or more serious games of course, which are always "table stakes", where a player simply goes all in and can only win the bets he can cover.
To signal going light, as you say, you drag chips from the pot in the amount you are borrowing, leaving them in front of you as a marker. But the money still belongs to the pot. If you win the pot, all is well--you just drag the chips. If you lose the pot, your friend is right--he gets all the chips AND you must cover your lights. Think of it this way--you're borrowing from the pot to make the call, and you're buying $6 worth of chips from the winner to cover your debt. You are out exactly $6 more than you would be if you had gone all-in.
If you had split the pot with him, you can short-cut the process by just giving him your lights and splitting the remainder, but that's for the advanced class. :-)