Why does my overhead door reverse after closing partway?
Most garage door openers will also reverse when closing if the force limit is exceeded. If the motor requires too much force, it will reverse for safety reasons.

It is possible that the force limit was set to low. It is usually adjustable via a screwdriver. But be careful, if you set it too high, you will defeat the safety feature. It should not be able to hurt someone seriously. 

If you still have the user's manual, it should describe how to set the force limit.

It is also possible that your springs weren't adjusted properly. If you disengage the opener, the door should be fairly neutral, manually put it half way down, it shouldn't want to go further up or down. The springs should counteract gravity. If the springs are strongly pulling the door up, hire a professional to adjust them. This is not a DIY job, the tension is enormous and you can seriously injure yourself.

Edit: While the opener is disengaged, you can also test for binding and lubrication as isherwood suggested.