Why did Krishna leave a body behind?

Krishna’s pastimes are multidimensional and fulfil multiple purposes. His disappearance pastime is known as asura-mohana-lila – a pastime specifically enacted to bemuse the atheists. For those who are stubbornly faithless, and who are determined to disbelieve in God, Krishna gives them reasons to maintain their doubts. It’s an amazing exhibition of Krishna’s ingenuity to create the possibility of atheism. Krishna designs the world and acts in such a way that people can argue Him out of the equation! He deliberately leaves room for explanations that (at least externally) seem to coherently justify an atheistic approach to life. In other words, He doesn’t make it a completely ludicrous proposition to not believe in Him.

There is an element of force in intellectually cornering someone. If you were obliged to believe in something it would be difficult to simultaneously put your heart into it. Since Krishna is ultimately interested in pure and unmotivated love, He endows us with independence and offers an array of options.