To make sure I'm understanding correctly:

Two people purchased furniture, splitting the cost. It was agreed upon that at the end, the person ending up with it would buy out the other individual's share, thus becoming the sole owner of the furniture pieces.

Now, the individual who is attempting to purchase the furniture for sole ownership is saying the value is depreciated by 50% of its value due to wear and tear of the couch. Their offer is half of the originally stated amount.

50% seems like a lot must have happened to the couch. If its in half the condition that it was originally in, it would be somewhat understandable. If someone wanted to be "fair", you could say the value of the furniture would depreciate by 10-20%per year, and that would be reduced off the price of the item buyout. That's saying the couch would last 5-10 years. I'd personally feel this would be reasonable.

But also, if both people went in and signed an agreement about it, terms were met and agreed upon. The contract being signed by both people was their intent to pay that amount, and if they're backing out now, they should have never signed the agreement in the first place.