Well I mean considering that Mr. Carson grew up in actual government housing in Detroit he at least knows what can be done to help and fix the system compared to most people who head the position and never actually grew up in government housing or had any idea what it was like..
I grew up in an agricultural area. Does that mean I automatically am fully able to become secretary of agriculture?
I mean Obama's current head of DHS never had 0 experience with anything Homeland Security related and was a lawyer so...t
Wikipedia told me Jeh Johnson served as General Counsel for the Air Force in 1998-2001 and then as General Counsel for the Defense Department from 2009 to 2012. His appointment was also related to the problematic state of that department that he was meant to solve.
Now, at the very least that gives him experience in working with government and safety services, while Ben Carson has been a brain surgeon. A genious one, yes, but has he ever worked in any position of public service, in any capacity? Of course, you're right in saying that a secretary doesn't necessarily require former expertise in his specific department. It's why you often see secretaries (Or Ministers as they are called in most countries) switching between departments - they have the set of skills and experience in government work that enables them to, with added knowledge and the help of deputies, serve well. Ben Carson has none of this. His appointment is the result of a purely political bargain.
