Proteins change shape depending on the pH. Imagine milk curdling by adding an acid, which is caused by milk proteins changing their structure due to lower pH. In the body, proteins make up various enzymes that drive all the essential functions of metabolism and regulation -- digesting food, producing energy, breaking down harmful product, etc. Human enzymes function best in pH of 7.4. If it deviates too much, enzymes cannot function anymore. Most importantly, glucose metabolism (which is how cells produce energy) will shut down and cells will die.
Acidosis or alkalosis affect electrolyte levels as well. For example, in acidosis where pH is low, the large amount of H+ ions displace potassium out of the cells, leading to hyperkalemia. I'm not sure what the mechanism is exactly but calcium ion levels are affected as well. Abnormal potassium and calcium levels will affect heart and neuromuscular functions.
Oxygen-binding of hemoglobin is also affected. In normal circumstances, hgb is supposed to pick up O2 molecules in oxygen-rich environment, such as alveolar capillaries, and drop them off in tissues where O2 level is low. Then, cells will take up the oxygen and use it for energy production. With low pH (acidosis), hgb's affinity for O2 decreases, meaning it can pick up O2 less easily. With high pH (alkalosis) the affinity increases and hgb will too tightly bind to O2 and unable to drop it off to cells where needed. Your preceptor was probably referring to this. If you want more details on this, google "hemoglobin dissociation curve."
So I think we can say that both acidosis and alkalosis lead to electrolyte imbalances, ineffective oxygen transport, and cellular disfunction, all leading to death.