The other replies have good examples. At it's simplest if you have $100 and go to the shops and leave with $20 you have not saved any money, you have lost $80. Reducing the amount you lose is not saving that money as money is still being lost. Yes you might lose less money than usual but the article and the point most people are making is that these offers short circuit rationality to make us think we are getting a deal but actually in most cases we are not. You have to be very shrewd to do the home economics correctly. I don't bother and most people don't bother and we are being swindled most of the time.
You aren't losing $80 if you are buying something that is of equal or greater value to you. No matter what, I am going to need toilet paper. If I usually spend $20 to get the toilet paper I need, and it is on sale for $15, I actually have saved money. Sure, I spent $15, but I didn't 'lose' $15. I saved $5. Even in the case of a bogo offer. I spend $22 to get 2 packages instead of 1. I don't have to buy toilet paper next month. So I saved $18 assuming that the time value of the additional $2 does not exceed the $18 savings by next month.
