A little crying is completely natural and probably even a healthy workout. But if he works up a real hard, gasping roar or wail, he's in real emotional distress that has physical and psychological implications. The large release of the stress hormone cortisol into the system during a cry like that has a direct effect on the brain, and repeated events actually change the size and functioning of some brain regions. Increased stress makes sleep more elusive, too. There's a fair amount of recent research on this; google "cortisol and infant brain" for more information.
To think of a one-year-old as "stubborn" may keep moms from recognizing that all behaviors (even in adults) are strategies to get some need met. Needs, whether physical (comfort) or emotional (connection) are legitimate; we all have them. But babies have very limited ways of making their needs known. Hard or sustained crying in a child so young is always a signal that some need is not being met.
That doesn't mean you can't gradually coach him to become accustomed to sleeping away from you. But I wouldn't do it "cold turkey," which could really tear away at trust and bonding, and result in an even needier, more demanding child. Or, what is even sadder, a child who has given up on getting his needs met, and learns to settle.
I learned during long talks with my mom that she let me and two of my younger sisters cry, quite a lot, apparently, because she thought that was the best way to train us. At least partly because of that dynamic, one of my sisters became intense and demanding (she was the "stubborn" one), and was constantly creating havoc in the family, in spite of extremely harsh and almost constant discipline. The other sis and I became sad, quiet, and apathetic. It took me many years as an adult to work my way through that early training so that I could take hold of my life and understand my deep conviction that it was never okay to ask for anything. Ever. From anybody. My childhood and young adulthood were hard, lonely, and sad. And I doubt that I will ever feel close to my mother. My sis joined Scientology to try to work through her issues, without much success.
I tell you this as a cautionary tale, and realize that all babies are unique and family dynamics add layers of complexity that cloud simple answers. I hope you'll keep in mind that the "habit" you are describing is really a pattern that you established and that your son has become reliant on. Your sudden decision to alter it won't make any kind of emotional sense to him.
Might you consider creating more space between you in smaller steps? For example, it sounds like his crib is a place that now represents separation and possibly desolation to him, certainly not a place of comfort and relaxation.
So, if he's currently in bed with you, how about having him spend some parts of the night in his own crib but near you, so you can quickly comfort him when he cries? As he adapts to that, extend the time periods in the crib. Once he becomes able to relax in his crib, you can move it to another room. As he matures, he'll be able to accept those changes better – in fact, many co-sleeping babies never have trouble making a transition to their own beds once they become more mobile and are able to use speech to express themselves and understand explanations.