For the seasonal salad at the popular Oz Kafe in Ottawa, the shavings of Gouda cheese are a salty and delicious culinary accompaniment. To the United States, they are an element of an increasingly bitter trade dispute over dairy products, one that threatens to undermine its decades-long agreement with Canada.

Canada’s longstanding policy of managing its dairy supply with production quotas and high levies on imports has become a sticking point in negotiations over the North American Free Trade Agreement, one that risks scuttling a 25-year-old pact that has stitched together the economies of Mexico, Canada and the United States.

President Trump has seized on the practice as unfair and insisted that he is willing to jettison Canada by the end of the week if it does not drop its dairy tariffs of 270 percent. On Tuesday, the chief trade negotiator for the United States, Robert E. Lighthizer, said Canada was “not making concessions in areas we think are essential” including “issues of dairy.”

But the melee over milk is puzzling to many trade experts. The United States supports its dairy farmers with a complex price support system that is economically similar to Canada’s system of supply management.

And while American dairy farmers may want to sell more milk into Canada, trade observers say access to a relatively small sector of the agricultural economy is not worth jeopardizing a trade relationship that has become critical to industries across North America.