Foods usually "go bad" because of the action of tiny organisms called "bacteria". These bacteria eat the food and poop out waste which can be toxic to humans. Bacteria also reproduce very quickly so even a few hours in the right conditions for their growth can result in dangerously spoiled food.

Cooking usually kills all the bacteria but it won't get rid of the poisonous poo, which is why you can't make spoiled food safe just by cooking it.

Raw chicken is dangerous because it can contain live salmonella bacteria which can make humans sick. Cooking the chicken kills the bacteria so they can't infect people, but allowing raw chicken to contaminate cooked items will result in people eating raw chicken and potentially live salmonella, which would be bad.

Cooked chicken on the other hand is safe to eat though so the raw chicken isn't going to be contaminated by touching it. Of course cooked chicken isn't safe forever so if the cooked chicken has had time to spoil then it can have a bunch of poison bacteria poo in it. There could also be a larger population of bacteria on the spoiled cooked chicken than initially on the raw chicken, reducing the time before the raw chicken spoils itself.