Why does marijuana smoke make me cough so hard?

Because its a toxin. The lungs were not made to inhale smoke, and if an irritant such as smoke is introduced there job is to try to get it out by causing coughing and increase mucous production. Be lucky that your lungs are telling you that they do not like it and please listen to them.
An Irritant. Marijuana smoke, and smoke in general is an irritant to the throat and the lungs. Your body, by coughing, could be trying to tell you: "hey, i don't think i like all of that smoke." you would probably agree with that, right?