The Constitution guarantees everyone charged with a crime the right to a jury trial. The impeachment process is a very narrow exception, where trial is by the Senate. That is because the impeachment has a very particular punishment: the removal of the official from office. A criminal court can’t impose such a political punishment, and thus it is reserved to Congress. Given that removal is the primary punishment in a case of impeachment, applying the process to citizens not holding an office they can be removed from makes no sense.
Supporters of prosecuting Trump point out that on top of removal, the Constitution also allows disqualification from future office as a punishment — exactly the reason they are prosecuting Trump. They argue that by including the penalty of disqualification, the Constitution authorizes the process to be used against anyone who could be disqualified from future office — which is everyone. The argument is self-contradictory: One could even more easily argue that the process can only be used when the primary remedy, removal from office, applies.