normal and sufficient blood flow to the body is designed to work under the normal effects of gravity. being upside-down for a period of time can cause lots of problems, mostly relating to the heart in specific, and blood flow in general. Humans are designed to work with earth's gravity- either upright or horizontal.
When you're upside-down for long periods of time, blood collects (pools) in places, most especially in the lowest vertical portions of the body at the time, like the face and head in general. If blood sits still long enough due to poor circulation, a clot can form. That's bad. This is why they recommend that you get up and stretch/walk around for a few minutes for every hour you spend sitting still, like on an airplane.
The human body is not designed for pumping blood out of the head and neck against the pull of gravity. Blood wouldn't drain properly out of the head and cause increased pressure on the brain. That's also not good. Between that and an increase in pressure to the vessels that serve the eyes, the optic nerves would have pressure put on them, which (to be brief) is not good.
So... those are a few reasons, in short explanation, of why we can't.
Why can bats? Because that's how their physiology is arranged to work.
