Why does "I am in your debt" mean the opposite of what it suggests?

I don't understand why if someone says "I am in your debt" it seems to mean the opposite of the literal meaning.

The person saying this says that they are in the debt of the person the phrase is directed to. A debt being "an obligation owed by one party (the debtor) to a second party".

So, if the first party says they are in the second party's debt, then should that not mean that the second party owes the first party something?

I totally understand that this isn't what it means... whereas this is the correct meaning...

I am indebted to you

Am I wrong? Or is the phrase "I am in your debt" totally wrong and misunderstood through relaxation of the term "I am indebted to you"?

Solution 1:

As noted at oxforddictionaries.com, to be in someone's debt means to owe something to someone.

For example, if you tell Tom, “I am in your debt”, you are saying that you owe a debt to Tom / are in debt to Tom / are indebted to Tom. As another example, a grateful but penurious person might say (to the person they owe something to, or are indebted to)

I am forever in your debt, and can never repay you.

Solution 2:

The issue you are confronting is whether the word debt (standing alone) refers to something owed or owing.

Imagine a reference to a "tax debt", does it mean that the national treasury owes you money or that you have an obligation to deliver some unpaid taxes?

So to be in X's debt, is equivalent to being indebted to X.

Solution 3:

One has to pay attn to ownership of debt.

A trio of shark loaners would meet regularly, Ahmed, Raghu and Shree. They would either trade or sell debts to each other. One day Raghu could not make it to the meeting and so he trusted some of his debts to Ahmed. At the meeting Ahmed pointed out to Shree a list and told him, "These are my debts, and those are Raghu's debts. We shall trade on Raghu's debts before trading on mine."

"OK, Shyam Chapati Co. is now in your debt, and we'll transfer Ghulam Herbs to Raghu's debt."

The passage illustrates how liberally we could assign grammatical possessive to the word debt.

With that in mind, a person could have a set of debt of honour owed to him and that set could be possessively assigned to him as his debts.

This is may not be how the phrase in someone's debt had dominantly developed, but having the perspective I explained would allay any sense of illogicality to the usage of phrase.