Why can I raise my left eyebrow independently from the other but not the right?
The muscle responsible for being able to raise both eyebrows is one and the same (m. occipitofrontalis). You can not raise one eyebrow because the whole muscle is connected to both eyes. It is possible that one side is not connected or less connected but that's usually not the case and such a person would not be able to raise both eyebrows at will.  

What happens in almost all people is that they are not raising one eyebrow, but instead keeping one eyebrow down and raising both at the same time thus giving the impression of only raising one. There are various muscles that are able to lower the eyebrows. 

So if one person is "not able" to raise one eyebrow, it actually means that they are not able to keep the other side down.