In my opinion, everyone can learn what they want, but what you should be thinking is the mastery, you can't perfect everything if you would not focus on just one craft. You will need thousands of hours before you could be considered as "master" on the specific field that you are into.
But, things like fixing your own things like your house, bikes, computer, I'm sure you can learn how to do it. Ever heard of "DIY"? I consider it self taught, but I can't consider DIY'ers as "specialist" that you are talking about.
There are also talented people who doesn't need someone to teach them, they could naturally enhance themselves by experience.