The Constitution is pretty vague about the criteria and process for impeachment. Most scholars (I think) consider “high crimes and misdemeanors” to be an 18th Century legal “term of art” (ie., a phrase that has a specific meaning in the in a particular context) that includes abuses of power by high officials.
On the abuse of power question, Congress (House and Senate) needs to draw the line somewhere. There probably ought to have been more laws, and more impeachments, over the years, to draw those lines. All presidents use their powers to improve their reelection chances. They all make policy choices based on what they think will please the voters and they spin, leak and lie to make themselves look better. But it’s a bridge too far when a president (or any official) uses his/her power to intentionally harm a political opponent, particularly when it impedes legitimate policy goals or undermines US national interests.
Between the official White House summary of the phone call, Trump’s subsequent statements to the press, and the government witnesses who testified, there’s more than enough evidence to conclude that Trump attempted to use US aid to Ukraine as leverage to get Ukraine to open an investigation against Biden’s son, that this was done to create suspicion about his political rival rather than some legitimate US policy goal, and that he did so in a way that undermined US interests.
The idea that the President was legitimately concerned about corruption with Joe and Hunter Biden is transparent BS. If it had been legitimate, the concern would have originated with and been pursued by the Justice or State departments, not just by Trump and his personal lawyer.
Congress doesn’t have to prove “beyond a reasonable doubt” that Trump did this, either. That would be the evidentiary standard from criminal law. Under civil law, on the other hand, the standard is “a preponderance of the evidence” (ie., it’s more likely than not). Impeachment is not a civil or criminal legal proceeding, so it is up to Congress to select (or not) a particular standard. But given the near impossibility of getting 50% of the House and 60% of the Senate to vote to impeach and remove – it’s never happened, after all – why would they make it even harder by borrowing the standard of evidence from criminal law?
The second charge is on shakier ground, but a wise move. Presidents have been expanding and increasing their powers at the expense of Congress for a long time, and Congress has largely rolled over and let it happen. Congress is supposed to make the big policy choices (ie., laws) and then make sure (through oversight) that those laws are faithfully enacted by the executive branch. They can’t really do that if they don’t have the power to compel testimony from executive branch officials.
The Supreme Court may disagree, ultimately. But it was important for Congress to assert this power. After all, the idea that the Supreme Court has the power to decide whether laws are constitutional isn’t explicitly in the Constitution, either: the Court asserted that it had this power by implication, and eventually the other two branches went along with it.
The House Democrats did the right thing. (On purely ethical grounds, they probably should have impeached Trump already for the content of the Mueller report.) It’s probably not good for most of them, politically, and there may be some negative consequences for the country in the short term, such as increased partisanship or economic uncertainty. But it’s good for the system itself, in the long term.