Pardon me while I speculate.
I find it hard to believe that President Trump doesn't know that economically tariffs are bad and protectionist policies are worse. But I think we can all agree that Donald Trump is a man of tremendous ego and nothing probably bothers him more than the idea of someone (or some nation) getting the better of him in a deal. America has gotten itself into a series of one sided deals over the decades and Donald Trump sees himself as the man who can fix this. I believe all of the above to be true.
Donald Trump is using tariffs as his cudgel to fix our trade deal with Canada. He will divide and conquer Canada with tariffs first on steel and aluminum then next on car imports to the US from Canada. A lot of "car jobs" flowed not just south to Mexico after the passage of NAFTA but also north to Canada. Those jobs left the US (the target market) because of lower labor costs but if the saving in labor were negated by import tariffs then GM and others would all have to rethink the utility of manufacturing in Canada (or Mexico),
Justin Trudeau has an election in a year's time and I think Trump is betting Trudeau will not sacrifice the Canadian economy (and Trudeau's election possibilities) in order to protect dairy farmers in Quebec.
Most people probably thought that with the passage of NAFTA there was true free trade between the US, Canada and Mexico. But that's not the case. Canada still protects some of their industries - most notably dairy and lumber - making those markets all but closed to US producers. With NAFTA expired I think Trump will offer Trudeau a deal of true free trade between the US and Canada without any tariffs or protections on any products. If he doesn't sign the deal then Canada gets tariffs instead with the hard to argue point of what's good for the goose is good for the gander and if there's one people who get geese metaphors...
A true free trade agreement between the US and Canada is a win-win-win-win situation. Most of Canada will see the price of their dairy products drop substantially and no longer have to worry about losing their jobs in an uncertain economy. This will help Trudeau (or whoever replaces Trudeau if he waits too long to act or if Canadians are put off by eye-browgate). Dairy farmers in the Midwest will all profit from all the new customers north of the border. And this will help Trump in his 2020 re-election campaign.
That leaves Mexico who it should be pointed out is not a G7 nation. I think NAFTA is dead and that the US will end up signing a separate deal with Canada. I fear that Mexico may be the next Venezuela if they move too far left in the next elections.
And remember how Trump promised Mexico would end up paying for the wall? That's what the tariffs are for.