There was no serious attempt to show that he committed a crime. Usually a crime is defined by some statute, and certain elements need to be proved in order to convict. And there is case law further defining what proof is needed.
There was none of that.
To the extent that there was case law, it all said that Trump had a free speech right to say what he did, and no one could explain why his speech was any more improper than similar statements from all the leading Democrats.
There was talk of elected officials being in danger for their lives, but that was all hearsay. There were no witnesses. No one testified that he was in any danger whatsoever. Indeed, the vast majority of the protesters had no intent to harm anyone.
One argument was that no crime was needed, and impeachment is a political act for removing a President who needed to be removed.
On Jan. 19, the Senate was in session, and Trump was still President. The Senate would have been obligated to hold a trial that day, if the House had delivered impeachment papers. Chief Justice John Roberts would have had to preside over the trial. The House leaders decided not to do that. Perhaps they thought that they would get some procedural advantage by waiting, I don't know.
Regardless, it means that the House chose not to impeach Pres. Trump. Impeachment occurs when the House delivers to the Senate papers to remove a federal official. That never happened. Instead, the House delivered some nonbinding opinion papers about a former official who is now a private citizen. the Senate could have ignored the papers, and 45 Senators voted to do exactly that. Chief Justice Roberts also decided to boycott the proceedings.
Left unresolved is whether the election was stolen. The Democrats main argument was the election was fair and legitimate, but they offered no evidence for that either.
The NY Times tried to put their spin on it, and ran the headline "Most Bipartisan Support for Conviction in History". That is because 14% of the Senate Republicans voted for conviction, 86% for acquittal. Another one complains:
But the way the House chose to frame the article of impeachment made the prospect less likely. If the purpose of the proceeding was to produce a conviction and disqualification from future office, as opposed to mere political theater, the House should have crafted a broader and less legalistic set of charges. ...So by this analysis, Trump was acquitted the first time because he was not accused of a crime, and acquitted the second time because he was accused of a crime that he did not commit.
The first impeachment of Mr. Trump was criticized (wrongly, in my view) for failing to allege a crime. But it is not necessary for an impeachment to be based on criminal conduct. ...
By charging Mr. Trump with incitement, the House unnecessarily shouldered the burden of proving the elements of that crime.