EMTs literally have the power of life and death. Make a mistake and the patient could be kaput, or at least in worse shape. Since no one is perfect, acceptance of these possibilities is a fact of life. However, keep in mind that if you are unsure what to do, you can always call upon the expertise of partners on scene and hospital staff by radio or cell phone. You don't work alone.
As an EMT, you also control the scene once you get there. The patient, friends and families, police, fire fighters, bystanders, and anyone else around will be expecting you to organize the scene and give instructions. For example, you might need family members or bystanders to help move a patient. You may need someone to calm the patient or a hysterical family member. You could ask a police officer to bring equipment from the rig. Even if a physician or nurse happens by the scene, chances are they will stand back and let you do your thing. You are large and in charge.
Your power is connected to your skill level. Intermediate EMTs get to boss around basics, and paramedics hold sway over both basics and intermediates. So the more you know, the more power you will have.
Experienced EMTs will be expected to help supervise newer EMTs. This task means molding a newbie into an effective team member. So you have to be able to critique a new partner without turning him/her off.