scylla is right. The border officers can deny anyone entry for any reason, visa exempt or not.
Because you are visa exempt, you may take it for granted that you can pop over for a visit but if the immigration officer has a reason to believe that you may overstay, that you may work illegally or simply are unsure of your reasons, they can deny you entry.
Many US citizens are also turned back when trying to enter Canada. In some cases, fiance's as well. Some have been told that they should not try to enter again without a steady job in the US and proof of that so the immigration officer knows they will return. I am sure the same is true for Canadians going to the US. Making a complaint is unlikely to accomplish anything.
Either apply for the fiance visa or go to Canada and marry him.
By the way, I knew a US/UK couple some 20 years ago. They had already planned their wedding. The UK fiance came to the US ready to get married and was turned away at the airport based on that if he wanted to get married, he should have a fiance visa and not try to enter as a visa exempt visitor. He went back to the UK, they applied for the fiance visa and got it. He returned to the US, they got married and still together now 20 yrs. later.