Our Founding Fathers wrote an "advice and consent of the Senate" into our Constitution. That means the president makes numerous appointments of his cabinet officials (your ministers) with the advice and consent of the Senate rather than on his own authority with no oversight. It can be a pain but it does help vet some candidates who should not be elevated to accessing the presidential ear. (Anyone remember Zoe Baird and Kimba Wood?) How Janet Reno slipped by still amazes me.
The idea is also that Congress has to work with the president's nominees and our Founders didn't want too much power invested in the Executive.
Here is another question for you then why was it not deemed therefore that the Cabinet Members are either Congressmen or Members of the Senate like our system why is it if some is a Congressman Or Member of the Senate and they are appointed to a Ministerial position they have to resign their seat?