There are only 3 ways to transfer heat into or out of something: radiation, conduction, and convection. A microwave, not surprisingly, uses microwaves (radiation) to transfer heat. It’s very easy to add energy through radiation. You just blast whatever it is you want to heat up with microwaves. The microwaves are absorbed by water, fats and sugars. Once absorbed, they’re converted directly into atomic motion, meaning heat.
To cool something down this way is another story entirely. Instead of just blasting something with microwaves, you have to hit it with very specifically tuned and timed microwaves to counteract and dampen the atomic motion. This is a very nice analogy: it’s easy to throw something at a bell to make it ring, but it’s a lot harder to hit it with something to make it quiet.
A “reverse microwave” would undoubtedly be an amazing invention. Right now, we waste a great deal of energy on cooling items, and keeping them cool. With a reverse microwave, you could cool that same item in a fraction of the time, using only a fraction of the energy. Though I’m afraid something like a reverse microwave might never exist. Active radiative cooling just isn’t very practical.
You might come across products that claim they can do it (e.g. http://www.ohgizmo.com/2013/10/29/reverse-microwave-chills-drinks-in-seconds/), but don’t be fooled. This impostor doesn’t use radiation at all. Instead it uses ordinary conduction & convection.