A steak is a solid piece of meat. Two sides of it have been touched by a knife. Contamination risk is low.
Commercially available minced meat has all been in contact with grinding plates, which may have been in contact with the flesh from dozens of animals since they were last cleaned. Everything throughout a burger has potential contaminant. This raises the contamination risk by several thousand times. You want to cook that stuff all the way through.
If you make your own mince using equipment you know its clean and in small batches then the risk is no higher than the steak you put in, and pink burgers are fine.
Food spoils because of bacteria, tiny little organisms which are practically everywhere. Cooking will kill those little guys off and the inside of a piece of steak is protected because there is no pathway for them to have worked into the interior since the cow died. Bacteria can’t just appear out of nowhere and the barrier of the meat means there is nothing in there to kill off.
Hamburger on the other hand is ground up meat. Bacteria can be mixed deep into the inside of a hamburger on the surface of the meat which is all mixed up, meaning cooking the interior is important to kill that stuff off.
With a steak, the germs that can harm us are generally on the outside and are killed by cooking.
On ground beef, the germs were on the outside, but when it was ground up, some of those ended up on the inside where they can survive cooking if the meat is not fully cooked.
I live in Canada and the “done-ness” of a burger is never asked here, they are always cooked through. However I’ve traveled quite a bit in the US and they always ask how I want my burger cooked. I guess the ‘Mericans are just bigger risk takers than us Canucks. 🤷
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