I can't speak for House Democrats although I can guess at their motivations. Instead, to address your query I will answer about my motivations.
I have seen clear evidence to suspect that Trump may have committed multiple offenses in violation of oath of office, national interest, and in some cases the law.
My interest is a fair and expedient process to evaluate whether sufficient evidence for such offenses is collected to bring to trial in the Senate. I desire for that trial, should it be warranted, to proceed in an organized fashion akin to a criminal trial where the relevant evidence has already been collected prior to trial. Thus, trial becomes about an organized presentation of that evidence both in prosecution and defense. And I desire for that trial to have the same due process protections for the exclusion of hearsay evidence and the opportunity for Trump to confront all the accusers who present evidence at trial.
In order to accomplish this, I feel the House has drawn up a very good process to proceed at this stage, and to move forward to trial at this point would result in a trial which is disorganized, cannot effectively establish truth without including hearsay, and would consequently violate due process for Trump.