Vnlr: ...
I live in one godawful country ...
This awkward, inefficient and plain silly custom can be found in many cultures all over the world. My Iranian landlord in the US used to tell me how retarded he thought that custom was in the culture of his relatives, he himself didn't practice the custom and was a straightforward type of person, reliable and simple to deal with. But it's not an exclusively Persian custom, you can find this social mechanic all over the world. I guess it is meant to give a safety buffer in case an offer was insincere but in my opinion, insincere offers either should not be made in the first place and if they are made, they deserve no merciful treatment.
In Switzerland, that custom exists on a private social level where people will politely refuse if e.g. a friend/colleague wants to pay for your drink, or they'll accept on the condition that they can take care of the next round. Personally I don't practice the custom. If I offer something, I mean it for real and don't need to hear any polite refusals. And if I'm being offered something, I'll either accept it or refuse it based on whether I want/need what was offered, not based on whether it is "socially ok" to accept or not. So if I want what is being offered, I don't fake-refuse.
I remember one time I was invited to my aunt's place for dinner and they kept asking me if I wanted second servings. I said sure every time they asked and ate everything they offered because it was delicious and I was hungry. Thrice they offered, and the number of times I devoured the offerings was three. Later on, my aunt complained to my mom that I had eaten everything and that they had intended to keep some of the food for reheating it another day. Tough luck, I eats all your food! And I don't feel the least bit greedy or guilty about it because I didn't actively ask for anything and assume that the offer is genuine.
Interestingly, the fake-refusal custom exists in Swiss private culture but not in the Swiss business world. Business matters are treated efficiently without much fanfare or prelude which makes it difficult for us to adapt to doing business in Arab countries as well as several other parts of the world where people spend more time with getting a feel for the other person and drinking tea etc before you talk shop. In our eyes, all that's needed is to A)
be there on time, B) assess the quality of the product and C) assess whether the price is a yes or no. If the price is not ok and there is leeway, both sides typically have one carefully crafted compromise worked out already and neither party will move much from their initial offer. Back and forth haggling is highly unwelcome.