Why was what Nixon did so bad that he had to be removed from office?
What Nixon did was so bad because it undermines the very core of our system of government. Our system of government is based on the idea of the rule of law. We are a "nation of laws, not of men" and Nixon's actions were contrary to that principle.
In our system, no one may put themselves above the law. We have limited government and the rule of law that is supposed to apply to all. We are not a dictatorship or some other form of government in which the ruler can act with impunity. That would be completely antidemocratic.
In the Watergate scandal, President Nixon used his power as president to try to put himself above the law. He used it to try to conceal illegal actions that were done for his benefit. It is hard to think of anything that a president could do that would be worse than using the power of his office to conceal crimes that were committed for his benefit. Therefore, what Nixon did was certainly bad enough to warrant removing him from office.