It wasn't so much the “never surrender” speech that finally set Hitler's teeth on edge and finally led to rage against Britain.
To be sure, Hitler found the bellicose Churchill exasperating, and much of this stemmed from the fact that Hitler quite honestly wanted Britain in his column, if not as an ally then at least one that would acquiesce to his geostrategic aims in Eastern Europe.
As the Cambridge historian Brendon Simms argues in his text Hitler: A Global History, the Führer regarded Britain and, for that matter, the United States, and by extension, the British Commonwealth nations - the dominions, as they were known at the time - as comprising the most successful branch of the Germanic race.
As he saw it, a struggle had ensured for centuries between two branches of this race - the Anglo-Saxons, the ancient forebears of the English, and the Teutons, the antecedents of modern Germans - and the former, significantly because of good geopolitical fortune, had excelled over the latter. These Anglo-Saxons had established a global empire on which the sun never set, and to add insult to injury, one of the colonial outgrowths, the United States, had supplanted the Mother Country of the Anglo-Saxon imperium as the most preeminent power on earth.
As Hitler viewed things, it was time for the Teutonic branch of the race to excel its own right, and through a stroke of strategic brilliance via one of his generals, Hitler had staged an end run (i.e., an attack through the Ardennes Forest) around the bulk of the French Army and the British Expeditionary Force. The end result was the rout of both armies and the entrapment of the BEF as well as a huge number of French troops on the beach resort town of Dunkirk.
Logistical concerns prevented Hitler from going for the kill, which enabled the BEF and some French troops to evacuated across the channel to Britain.
At that point, Hitler was confident of victory in the West. France essentially was finished, and Britain had no other choice but to save face with a negotiated settlment, whereupon it would be forced to adjust itself to the new order in Europe and the need to concentrate all but its exclusive focus on overseas empire.
Consequently, Hitler likely viewed Churchill’s “Never Surrender” speech as mere rhetorical bluster.
It was only after the Battle of Britain had begun and Hitler was served the painful realization that Britain would remain in the struggle for the foreseeable figure that his rage against Britain took hold of him.
Britain's continued presence in the war would hamper his greatest of ambitions, which was invading the Soviet Union, conquering the land west the Ural Mountains, and building a continental empire populated by German farmers that rivaled Britain's predominantly maritime empire.
Churchill’s determination to reciprocate German aggression through aerial bombing raids only served to stoke Hitler’s anger and his determination to exact revenge.
