And would it have made a big difference in the war if he didn't?
In Dunkirk: Retreat to Victory, Julian Thompson argues that it was a combination of Hitler's poor strategic ability and Goering's persuasiveness.
Almost form the moment that Army Group A broke through at Sedan, Hitler developed something of an obsession with the left flank of the group being exposed to a counter-attack. Although it was a legitimate consideration, he misappreciated the situation and didn't listen to the observations of front-line commanders who knew that there was no secret Allied army massing in Eastern France and ready to strike.
For these reasons he issued two stopping orders to Army Group A, much to the irritation of its commanders, to prevent them from advancing too far too fast. This isn't completely unreasonable, the plan had run almost like clockwork up until this point and it is highly unusual for an operation of this scale to run so smoothly. Where Hitler showed his naivety was by ignoring his commanders who knew the situation on the ground; this is where Goering steps in.
As the net closes around Dunkirk, Hitler is still concerned about the risk of a bloodbath and Goering offers a quick, clean solution: the Luftwaffe can destroy the BEF from the air. Hitler buys the argument, but it is fundamentally flawed and highlights Hitler's poor understanding of air power and either ignorance or self-service on the part of Goering.
There is no chance that the Luftwaffe can do what Goering says, even the large bomber forces of the later years of the war would have been unable to achieve it and even a modern commander would be foolish to try and destroy an entire army from the air alone. The result, of course, is that the BEF and a number of French and Belgian forces are evacuated, but Hitler remains oblivious to his own failings, sells the fall of France as a great victory and convinces himself that he is a great strategist. Arguably the hubris Hitler develops from this leads to his overconfidence invading Russia a year later.