This question has raised a number of points
1 Why not give in at Verdun? Verdun is in France. The French had been invaded by the Germans for the second time in living memory. Verdun had been the last fort to hold out in the Franco-Prussian War. Imagine if the invasion had been of England. Would you be surprised if the Army command and popular sentiment had insisted that York or Canterbury should not be surrendered without a fight?
Verdun was much less significant militarily than as a symbol. It was chosen by the Germans specifically as a place that the French would be bound to defend with the intention of "bleeding France white". The eventual casualty bill was around 550,000 French to 440,000 Germans, about half of them in each case killed.
2. The generals on both sides were anything but incompetent, but Verdun was exposed on three sides and until the introduction of tanks late in WWI a static position like Verdun was doomed to be a killing field for both attackers and defenders.
3. Britain, and therefore Canada, Australia, New Zealand , India and all the other countries of the (then) Empire were only involved in WWI because Germany chose to attack France via Belgium. Regardless of the truth or severity of atrocities perpetrated by the German forces in Belgium (and there was a commission to investigate these claims which concluded there was a case to answer), Britain had a treaty to go to Belgium's assistance in the event of an invasion. This was one of the interlocking treaties which diplomats across Europe had put in place to make war unthinkable. Unfortunately once war had started these same treaties ensured, like a set of falling dominoes, that the resulting conflict involved practically everybody south of Scandinavia with the exception of the Swiss. There was never any possibility that Britain would have entered the war on the German side.