Recently, I had occasion to make a left turn onto Runnymede Road from a two lane local street. To allow cars making right turns to pass me, I had pulled over to the left side of the lane, then a car pulled onto the right side of my bike with its left turn signal going.
I accordingly pulled out in front of the car, and when the road cleared, I pushed off, making sure I stayed in front of him.
The safe and courteous way for cyclists and cars to share the road in a left turn goes like this: the cars and bicycles go in the order they arrived at the intersection. When a bicycle turns, the cyclist rides ahead first, making a wide, "L"-shaped left turn, which leaves room for the car to proceed through the intersection. That way, the car turns into the left lane (or the left side of a single lane), and the bicycle turns into the right lane.
A car which tries to pull out to the right and turn to the left will cross paths with the route the cyclist would normally take to turn left and reach the right lane. Experts on bicycle safety warn cyclists to avoid situations such as this. As the diagram to the left shows, the car and bicycle tracks overlap in this situation.
So why insist on proceeding in order? Why not just allow cars to go first? Two reasons: I ride my bicycle for much the same reason most people drive: I have somewhere I want to go. I want to get there safely, and I also want to get there today. If I get off the street and wait for all the cars to go by, I will never get anywhere. Also, the rules of the road, including having vehicles proceed in order, makes traffic movements predictable and therefore safe. When some cars queue up safely to turn, and others pass in violation of the laws, other road users lose the ability to anticipate the movements of other vehicles. Treating cyclists as vehicles (as the Highway Traffic Act requires) simply makes everyone safer.
On the subject of safe turns... if you pull up behind me while I wait at an intersection, I will look to see if you have your right turn signal on. If you do, I (and most cyclists) will move left or right if we can do so safely so that you can turn. If you do not signal, I can't tell what you want to do.