Do you have backface culling turned on? Try it if not.
I do actually.
Sanity check, when you load it in your program do you have 24 vertices and 24 texture coordinates?
I'm guessing you have less vertices than texture coordinates, in which case you need to weld your vertices. Basically, for each unique vertex + texcoord combination, you need to create a unique vertex (because obj files have separate indices per component, but OpenGL only supports a single array of indices).
See I was wondering about that, that seemed weird. So welding vertices huh? I'll have to research that. Thank you so much! That makes perfect sense!