Mr. Miskatonic has it right, in my opinion.
Think about it- the President is one of the most powerful men in the entire world. By his orders, the army marches, laws are approved or vetoed, rules are enforced, the button is pressed. We have an entire division of the government devoted to protecting him (well, that and stopping counterfeiters).
And yet some loser with a mail-order rifle can kill him.
What does that say about our security? If the President can get taken down, how likely are we to get knocked off in a random shooting? What does that say about our government, when we realize it is only by social convention that it actually works, and that were a few hundred people so suicidally determined, they could off the entire Senate?
Thus, people invent and cling to conspiracy theories. Surely, someone as important, as guiding, as luminary as Kennedy simply couldn’t have been taken out by a random whacko; such is the path of nihilism. No, he must have been killed by powerful people, possibly as or more powerful than him, who opposed the good things he was doing. The Mob, the Russians, the CIA, etc., etc., etc.
Such theories have popped up around nearly every in-office Presidential death. Zachary Taylor was poisoned by arsenic in a scheme cooked up by influential Whigs to ensure the safety of the Compromise of 1850. John Wilkes Booth was in the pay of someone else, possibly the Confederate government, who hoped it would force a peace; possibly Secretary of War Edwin Stanton (who burned his personal papers regarding the investigation), who wished to force a coup and take over the government. Guiteau may have been crazy, but he was led on by anti-reform Republicans who wished to stop Garfield. Czolgoz was the first part of a vast Anarchist strike to cripple all of the Western governments. Harding was poisoned by his wife so that she would no longer be embarassed by revelations from the Teapot Dome Scandal.
I think Franklin Delano Roosevelt and William Henry Harrison are the only Presidents who died in office without someone later positing the theory of a conspiracy to murder them. Probably due to length- with Harrison in office for 30 days, no one knew him well enough to hate him; with Roosevelt in office for 13 years, anyone who wanted to kill him would have done so a lot earlier.