But that doesn't mean the courts will side with me and not you. Strict logical coherence isn't always adhered to. It's even been called "the hobgoblin of little minds" - so perhaps Emerson would take your side on this.
You don't make the mattresses yourselves, you purchase from a manufacturer and sell in your storefront. There are only a few different mattress manufacturers.
Your rival, instead of adjusting prices or organizing better marketing, simply plays the manufacturers not to sell to your store for six months.
Unless you can rapidly find a brand new source of mattresses or have a very healthy rainy day fund, you will likely go under fairly quickly after selling your remaining stock.
This leaves only one store in town, and they can set the price to whatever they want. Now that they are the only established incumbent they can easily recreate this scenario with any new mattress stores that want to open in your city.
Now the people of your city have only one store for mattresses, and have to pay whatever is asked for. This is not because the business did anything especially well to win more customers, or because you did anything wrong. They simply destroyed the competition through anti-competitive behavior and have negatively affected everyone else in your area.
This is why it is illegal.
As well, although this may not contradict what you intended to say: patents, for example, precisely grant "the right to exclude." Exclusive territories are a frequent way to do this. So in that case, it isn't necessarily illegal.