> Apparently, the president can shut down half of the government departments via executive order. How? Because they were created by executive order.

Please list the departments and cite the executive orders creating each, because I think you will find that this is far less than half (and, unless you are using a non-standard definition of what constitutes a department in the US federal government, that the proportion is actually 0%.)

(A sibling commenter has demonstrated that the single example you provided is wrong, but its not just a poorly-chosen example.)