Strange - usually it's the other way around (will read manufactured CDs, but not home burned).
Do you have another drive to try in it's place?
I have seen it before though and it's usually been that the drive is dying. Either something is preventing some CD's from spinning or the lens is damaged in some way. If you want to take the time, take apart the CD drive (it's pretty easy) and clean the moving parts.
Just take the time to remember how it came apart! It makes it easier to put it back together.