You don't. There is not a lack of privity, most likely. On the underlying debt, you agreed to let them assign the debt should they want to. What that means is that they have the right to assign their right to be paid under the debt to another company, and even though you did not enter into a contract
with this third party, you are still legally required to pay them (but only under the same terms and conditions as the original contract; nothing but the payee changes in that contract). I wish that I could give you better news, but this is the law, and the courts are not going to turn over hundreds of years and thousands of cases of established precedent now. This is literally the law all over the world. If they have the right, contractually, to assign the interest to getting paid, then they can do that.
Now you might have some other defenses, such as statute of limitations
. This varies depending on the debt, but for instance, if it is an open account (such as a credit card) then if it has been more than 4 years from when you stopped paying until when the collections company sued you, then you can claim the defense of statute of limitations.
Otherwise, if the lawsuit was filed during the statute of limitations, then based on the limited facts that I have, you're not going to have a valid defense to stand on here (to absolutely win, that is).
I know that this is probably not what you want to hear, but it's the law. I hope that it clears things up anyway. Good luck to you!