Why is everyone trying to ram me?
Usually when you're running a Vehicle Theft side mission, as soon as you get the target car, the cops are going to chase you.
Other drivers on the road react to police cars in unpredictable fashion - the most common thing they will do is attempt to "pull over" when police cars are approaching.
Unfortunately, the logic for "pull over" isn't always intelligent. They'll often pull over in front of you as opposed to pulling over to get out of the way.
There's not much of a way to get around this sadly. You just have to drive fast so that you pass them before they have time to react, and pass with as much lateral distance between you and the other cars as possible. The "Nitrous on every car" upgrade can be useful here as well.
As a side note, they will react the same way if you're driving a vehicle with sirens and turn them on. Often times the unpredictability of this yields so many issues that it's not worth using the sirens in these vehicles at all.