Well, as a psych student I can definitely see where this issue would stem from. Therapists really aren't taught too much in depth science stuff (unless you deviated from or take on a more science-based path or psych program like I'm doing). Some of my friends that are in the B.A. psych program, get away with no biology beyond a high school level, biochemistry, calculus, etc. but they are great at handling things like relationship issues and helping people with phobias, etc.
The science behind ME is also very new (and constantly being updated) so even if you are a world class scientist, you have to stay up to date with everything. Some of my psych classes are basically composed of you reading a huge textbook and memorizing it so you can spit up certain facts on the test. You can be a really bad people person or have little passion for the field, but still become a therapist if you have a good memory. I'm not saying this is true for all therapists, but it does happen.
As with any professional, it's hard to relate to something you've never experienced. Having the academic experience learning about a disease and it's psychological impact on the victim is great, but experiencing it is the only way you can truly understand how it feels. Your therapist can't relate to it like you can, and that's with any disease. An oncologist that has never had cancer can treat a patient with their knowledge, but can't relate, just like a male obstetrician might be one of the best at delivering babies, but he has no idea what it feels like to be the mother-to-be. The same thing for therapists. While they can be great, you have to keep in mind that they have their limits when it comes to empathy, and not all of them are as science minded as you'd think. I think the best therapist to talk to about CFS issues would be a therapist that has research interests in it, has experienced it, or like you said, has someone close to them with it. It might also help to see a biopsychologist or a neuropsychologist since they have more knowledge on the science aspects of things like CFS and the neurological system, yet they're also trained to understand the psychology side of it that some physicians aren't as good at. I know some of the medical doctors I've been to are far from people people (like socially awkward/stereotypical nerd) and sometimes a bit cold.
If you are christian or Jewish or anything, a pastor or rabbi, etc. can be helpful to talk with.
Of course there is this board if you want to discuss something on here.
All the best!
Lilac