I think most people can learn to sing. I used to have really bad intonation issues. I found that most of my intonation issues were due to poor technique. I knew what notes to sing, but my technique got in the way of my singing.

I had to learn to "feel" when I was singing properly because it all sounds the same to my ears, although I can hear the difference on tape. I was trying to control my voice but I found that I really had to just let it go where it wanted. With some freedom (I'm still not completely free) I have gained a fourth in my upper range and a few notes on the bottom. I used to be able to vocalize from g below the staff to g at the top of the staff. Now I can vocalize from e below the staff to high c.

If you really want to learn to sing you need to find a teacher who can help you. I don't think you can learn it on your own. But I wouldn't say you can't learn just because you can't teach yourself.