Impeachment in the United States is not like a simple vote of no-confidence like in other countries. The Constitution provides for impeachment only for "High crimes and misdemeanors" committed by public officials. So although it is a political process, the Constitution deliberately sets a high bar that rises to the point of criminality in order to remove a public official from office.
In other words, a public official must have committed an impeachable offense in order to remove them from office. You cannot simply unseat them for mere political reasons. Exactly what constitutes an "impeachable offense" has never been specifically defined, but being despised by the opposition party is definitely not one of them.
The idea behind this is twofold: Firstly, the co-equal branches of government are supposed to provide checks and balances upon one another so that a relatively broad base of consensus among politicians is required to function. And secondly, politicians' limited terms, with their offset election cycles, is supposed to ensure that bad things done in one cycle can be undone in another cycle if they're so politically unpopular. Basically, a bad president is supposed to be prevented from doing bad things by the other two branches, and if bad things do happen, you only have to live with it for a couple of years. All this is part of the normal political process.
To bring this back to Trump (which is why impeachment is such a hot topic right now), the United States is currently living in a state of unprecedented division between the political left and the political right. If the Left is correct, and Trump actually did commit the treason, collusion, and obstruction of justice that he is accused of, then that is an impeachable offense and he should be impeached for it. However, if the Right is correct, and all these accusations are a witch hunt from a party suffering from the throes of Trump Derangement Syndrome, then he should not be impeached. If Trump is such a terrible president, then that's what elections are for.