President Trump pardoned Joe Arpaio because he likes the cut of Arpaio's jib.
He pardoned him because he knows it'll play great with his base. He pardoned him because Arpaio was an early political supporter and because Trump rewards loyalty. He pardoned him because Arpaio provided Trump with a rough blueprint for demonizing Obama, immigrants and minorities as a means of achieving electoral victory. He pardoned him because he shares Arpaio's contempt for laws, courts and political and legal authority that belongs to anyone but himself.
Like anything else Trump does, it was done based on a gut feeling and a selfish desire. If there is any doubt about that, one need only look at the way Trump bypassed the customary pardon process which involves review by the Department of Justice. There was not a ton of thought and analysis put into this. It was a purely personal, purely political act.
In light of that, anyone trudging into the weeds to frame this as some complicated interplay between the branches of government, the nuances inherit in the separation of powers or any of that stuff is selling you a bill of goods. They're doing this either because they support Trump or because, even if they do not, they support people who would have to do something about Trump if the pardon comes to be seen broadly as the disgraceful act that it truly is. When you're a Republican -- even a #NeverTrump Republican -- the last thing you want is for the people you do support to have to spend any time or political capital opposing Trump, because that takes valuable time away from cutting taxes for the wealthy and hamstringing the government's ability to, you know, govern. It also makes them worry that they're committing religious heresy.
But really, it's a simple case. Arpaio and Trump share supporters and share enemies and at a time when Trump feels that he's under attack, he's going to do whatever he can to show strength, to prove he has allies and to rally whatever support he feels he can rally. And make no mistake, he'll rally a lot of people to his side with this pardon because he and his supporters will couch it in terms of "law and order" -- Arpaio was a sheriff after all! -- and people eat up appeals to law and order.
Unfortunately, the growing public conception of law and order is twisted and corrupt. Indeed, "Law and order" has quickly become synonymous with "police," and any effort to oversee and check the power of police is seen as hostile to "law and order." This includes civilian political authority and the courts, which politicians and, increasingly, the public, have chosen to portray as an impediment to law and order as opposed to a necessary component of it.
In this, such vocal support of "law and order" is in direct opposition to the rule of law, which requires checks on the power bestowed upon men, particularly the coercive power of government as manifested in armed police forces. It's a craving for the "order" without the "law." People want cops to "get the bad guys" but increasingly have no respect for the process by which "bad guys" are identified and handled and refuse to accept that the police themselves can ever be "bad guys." Such a view is anathema to a functioning civilian-led democracy. Indeed, it the very definition of authoritarianism.
Which brings us back to Donald Trump and Joe Arpaio. To the extent you approve of this pardon, you approve of a leader using his extraordinary power to vindicate his personal obsessions and to reward his allies. To the extent you believe Arpaio was deserving of this pardon, you do so because you believe that the power of police should be absolute and that the power of the courts to rein in that power is illegitimate. You, quite simply, approve of an authoritarian government.