The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors
There is a minority view that federal judges can be removed some other route given they serve during good behavior. After all, other federal officials can be removed in various ways, including in some cases by another removal process. Mentally unfit judges are another interesting thought experiment. In extreme cases, lower court judges have been denied the right to hear cases for a limited amount of time.
I think there is some validity to this alternative but it's theoretical given long practice and likely court review. The likely process is that a federal judge will be convicted of a crime and then removed by impeachment. A few judges were removed in other cases. Ethical rules are another way to enforce the Good Behavior Clause. So, it isn't impeachment or nothing.
Impeachment was used a few times against presidents, leading one president to resign before the process played out (Nixon). It was used against a senator but the final result made it unclear if people thought senators could be impeached. It was used against one Cabinet member. He was not convicted. OTOH, the trial continued after he resigned.
William Belknap earned his impeachment. Homeland Security Secretary Mayorkas did not. He regularly showed up in front of Congress. [Compare Trump's stonewalling that led to an impeachment count.] Congress tied his hands by not providing enough funding. Efforts to pass legislation are being blocked for political reasons. The current House impeachment campaign is best explained as a policy dispute.
Some liberals are strongly against President Biden's border policy. Overall, I think this is a mix of not giving him enough credit for some of the stuff he did and an unrealistic judgment of what he can do in the current environment. Yes, I wish he was more liberal. He's not a lefty. He's overall a reasonable moderate with some lefty positions (he has been strong on labor in multiple cases). Also, the country at large is more conservative than his critics wish. You take what you are offered here.
Some people argue that basically whatever a majority of the House decides can be impeachable. There is a text that provides specifics. You can say that the law is whatever five members of the Supreme Court say it is. That is a bit blunt. We can also say that the body interpreting the Constitution (or whatever) is being unreasonable. I think that is a valid approach.
I think -- without doing a deep dive (I might do more if this actually passes the House) -- the House Republicans do not have a case. They are using impeachment to go after maladministration (what we are told impeachment is not for) and politics. You use the tools available, even if it is shoving a square peg in a round hole. Still, there are levels here. They do come off as hypocritical and cynical partisans if we look at it as a whole.
They are charging him for not enforcing the law even though he is following the bipartisan policy of enforcement discretion. A general abuse of power claim also doesn't hold up. Homeland Security, if anything, has engaged with Congress more than other departments have. This is symbolic of the whole thing:
Ahead of the hearing, House Republicans and DHS clashed over whether Mayorkas will appear in person during the impeachment proceedings. Republicans wanted Mayorkas to attend this week's hearing, but he declined, citing a conflicting meeting with Mexican officials about border enforcement. The secretary agreed to testify, but asked to coordinate a time that works for his schedule.
The test under the impeachment clause is so vague and open-ended that I am not totally sure you can say they are blatantly violating it by charging him this way. It likely at least violates its spirit. It also is a horrible approach as a matter of discretion. All three factors in here.
There is also the politics. It is in Trump's interests to keep the border issue on the table as an issue. A bipartisan bill therefore is not in his interests. It is somewhat less clear how useful this all is for swing-seat Republicans. They continue to be tainted by the stink of the overall clusterf- of this House of Representatives. I doubt Senate Republicans, who have a good chance in November and want to appear more reasonable, want a trial.
It has passed the committee and is now going to the floor.