Is it possible to become a specialist studying by yourself?
Self-education is great! There are thousands, probably millions, of things we can learn throughout our lifetimes without needing to sit in a classroom.
The thing with our society (US) is that we want proof before we let someone open our chest cavities, connect our electrical circuits, cut down our trees, or advise us in investments. Going through a program of training, whatever it may be, provides us with a document that says we were trained to do these things. People want the assurance that the person cutting their hair or decorating their home knows what shes doing.