Theresa May has seen the future, and the British Prime Minister seems to think it looks like Canada. So have her opponents in Brussels: They see a much darker sort of British future reflected north of the 49th parallel. In the Brexit feud, free trade with Canada is simultaneously the dream and the nightmare, the alpha and the omega, the proof and the refutation. Canada’s mammoth trade and investment pact with the 28-country European Union, the Comprehensive Economic and Trade Agreement, was signed last year but still has to be ratified by European member parliaments. That hasn’t stopped it from becoming a prop in Ms. May’s campaign to win the June 8 British election. CETA is her answer to those who point out she has no viable plan to fill the enormous hole that quitting the EU will create in the British economy. In the view of Ms. May and her deputies, CETA shows that countries outside the EU can easily negotiate their way into the bloc; it is also, they think, just the sort of agreement Britain can negotiate quickly with outside countries to make up for lost income. She recently discovered that CETA can be used against her. In her infamous dinner last week with Jean-Claude Juncker, the president of the European Commission, Ms. May repeatedly made the claim that Britain will be able to negotiate its way back into the EU’s common market almost immediately after quitting the group. She even suggested (according to the detailed description of the dinner provided to the German media) that the EU trade-deal negotiations begin before the Brexit talks (which will take years) are finished – something the EU countries have unanimously ruled out. In response, Mr. Juncker reached into his satchel, pulled out the full 2,000-page published text of Canada’s CETA deal, and placed it on the 10 Downing St. dining table. This thing, he pointed out, took 10 years to negotiate and is still not finished – and it’s a deal between two parties, Canada and Europe, that eagerly courted each other, not two that have just concluded an acrimonious separation. He reportedly told her: “I think you underestimate this, Theresa.” Yet, the myth of an easy CETA continues to drive Theresa May’s campaign. She frequently points to a report issued by the pro-Brexit think tank Open Europe, which claims that Britain can safely leave Europe’s customs union and quickly replace almost half of the obliterated trade income by negotiating its own deals with outside countries, including Canada – and then negotiate its way back into Europe equally rapidly. In fact, it suggests CETA simply be duplicated and passed in months. Indeed, as if this were realistic, Britain has pushed ahead with it, arranging at least three meetings between Canada’s International Trade Minister, François-Philippe Champagne, and his British counterpart, Liam Fox, to discuss the possibility of a Canada-Britain trade deal. Mr. Champagne and Finance Minister Bill Morneau have both said they’d welcome a Canada-Britain deal should Britain leave Europe. And why wouldn’t they? Such a deal has been sought for almost a century by Canadian prime ministers, fruitlessly and, largely, pointlessly: Only a sliver of our trade is with Britain, and half that trade is made up of diamonds and gold, for which London merely serves as a waypoint into the continent. In fact, most of Britain’s trade value to Canada is a result of the Britain’s EU membership. I spoke to several people involved in the CETA negotiations this week, and they all said that a similar agreement with Britain, even a rush-rush duplicate deal, would likely take at least four or five years – especially since Canada’s trade department is deeply tied up with China, a potentially renegotiated NAFTA and the complex final steps of CETA itself. Any deal with the United States would take at least a decade, assuming it could ever pass through the very trade-hostile Republican Congress. And a deal with Europe? It would happen, eventually, but it would not be fast or easy. Stripped of her CETA prop, Ms. May is the most paradoxical figure: A politician facing an election she can’t lose, fought over a deal she can’t possibly win.