Under the Constitution, there are several steps between impeachment and removal. It is up to the Senate to conduct a trial on those articles and then to decide, by a two-thirds majority, whether the president should be convicted and removed from office. The Senate vote to convict Johnson after his trial fell one vote short. Richard Nixon resigned in 1974 before the House voted on articles of impeachment, so he was not impeached. Advocates of the message almost certainly did not want the process to end with the approval of articles of impeachment, but rather to continue to removal of the controversial chief justice, whose opinion in Brown vs. Board of Education ordered desegregation of public schools.
Impeachment sounds terrible.
It has also been linked to the Latin impetere, to attack or accuse. In less momentous times, the word is more often used in the sense of impeaching a witness in a trial, or casting doubt on his or her credibility.