This question originally appeared on Quora. 
Answer by Ross Cohen, EMT
Yes, you should. Please do.
Short Answer:
Our goal is to bypass traffic as quickly as possible to potentially save a life. The challenge is that driving to an emergency through heavy traffic with lights and sirens can be dangerous. Stopping completely eliminates that danger.
If everyone on the road stops, we can zoom by, safely and efficiently. If some cars keep moving, even slowly, it can slow us down. More cars moving creates more variables; it reduces our choices for avenues of travel and it forces us to drive much more cautiously. Both have the effect of slowing down response time, which in a true emergency can cost someone their life.
Detailed Answer:
If cars are still moving, we have to exercise extreme caution and due regard for the safety of others, particularly when passing, when going through red lights, when going against a one way, when turning left in front of oncoming traffic, and especially when crossing a double yellow line.
For example, right next to the ambulance headquarters of one of the agencies I've worked for is an extremely busy intersection. It's two minutes off the highway and within 100 feet of shopping centers in all directions. It has turning lanes on all four sides which tend to fill up. Leading up to the intersection is a single lane that merges into the turning lanes, causing traffic to back up for quite a ways.
Even with lights and sirens, getting through this intersection during rush hours or lunch time is tricky and fraught with hazards. If vehicles coming from the other direction don't pull over, I can't safely cross over the double yellow line to bypass the jammed lanes on my side. Without crossing over into the open space that would be created by their pulling over, the ambulance is slowed to a crawl as each car on our side slowly pulls a few feet to the right, one by one. First the car in front of you pulls a couple feet into the next lane before they have to stop and wait for the next car to do the same, who's in turn waiting for the next one to make a small opening for them. As you might imagine, it can be very distressing to be dispatched to a "Child Choking" and have to wait for this painstaking process. Our sirens are blaring, our hearts are pounding, adrenaline is pumping, yet our vehicle is stuck, gingerly drifting by these cars like a lily pad on a pond.
Best Case Scenario:
All cars from all directions pull over at once. We zoom by in seconds.
Worst Case Scenario: (excluding collisions)
Only the cars in our immediate path attempt to move. It takes us minutes to wait for our opening and thread the needle. When we finally get through, we're not only delayed, but we're frustrated and worried and potentially more careless with the driving ahead.
Most of the time, it's somewhere in between those two extremes, but it can be better, and don't forget we still have more intersections to negotiate.
There are driving tactics some emergency vehicle operators employ that can *encourage* the traffic from the other direction to pull over, such as crossing the double yellow more aggressively and scaring them, but that obviously carries its own risks. Pull over no matter what and we'll zoom by in no time.