Stuck In The Middle

Imagine the globe. No matter where you stand on the globe, your feet will always face the center of the Earth, right? Ok, now dig a hole straight down from anywhere on the Earth. What happens when you reach the other side? You don't fall out because you just said that your feet are always on the ground...but if you flipped over some where during your digging you would have fallen back towards where you started. Isn't that weird?