Well, I am primarily a vocalist. Guitar is new to me, I've played sax for a while, but I consider voice as my primary instrument. And, I don't know that I'd agree with "Anyone can be taught to sing". One thing that I've really realized over the last few years of training is that singing is playing an instrument just as surely as guitar. It's not JUST your vocal cords. It's also resonance in your chest, your face, your head, your throat.....

And, it might be that your body is just not shaped or designed to sing?

I'm curious, have you ever taken any vocal lessons? They can be very helpful in teaching you to use the "instrument".