Suppose that within the next few months, it becomes clear that President Donald Trump has committed impeachable offenses. Does the House of Representatives have discretion to decide whether to impeach him? Or does the Constitution require it to do so?
The simplest answer, and the best, is that the Constitution requires the House to do so.
To avoid political bias, let's bracket all questions associated with Trump, put current events to one side and assume that some future president commits (in the words of the Constitution) "Treason, Bribery, or other high Crimes and Misdemeanors." Imagine that he has betrayed his country, in a way that constitutes treason, or that he has killed or imprisoned journalists and political enemies (clearly a high crime and misdemeanor, and so an impeachable offense).
The Constitution says that the House of Representatives "shall have the sole Power of Impeachment" and that the Senate "shall have the sole Power to try all Impeachments."
In light of the historical background, use of these powers is best regarded as mandatory rather than optional, at least when a president has clearly committed impeachable offenses. To the founding generation, the impeachment provisions were essential parts of the Constitution.
As Virginia's George Mason put it at the Constitutional Convention: "No point is of more importance than that the right of impeachment should be continued." (It is worth pausing over that sentence.)
The power of impeachment was designed to ensure that our system would be one of self-government. It gave We the People an ultimate weapon in the event that the president violated the principles embodied in the Declaration of Independence: "A Prince, whose character is marked by every act which may define a Tyrant, is unfit to be the ruler of a free people."
For this reason, it is wrong to say, as many now do, that the Constitution makes impeachment a political question rather than one of law. On the contrary, the Constitution sets out a legal standard, which establishes a very high bar, and which forbids impeachment on purely political grounds. At the same time, the Constitution specifies what has to happen if the constitutional standard is clearly met.