Because chickens are strong and have sharp beaks, and even if they manage to overpower a chicken it will hurt. As long as the cat has enough food it probably won't try. A large rooster would be able to win a fight with a cat.
Also, cats usually won't go after anything that's willing to face the cat down, even smaller animals like rats. I have both cats and rats and the cats will watch the rats in fascination, and even sniff noses with the rats when I have the door to the cage open, but the rats show no fear to the cats, and will even rush the cage bars if they decide a cat is too much in "their territory" and the cats respect that. This has held true through 8 different rats so far, and like 6 or 7 different cats (mine and various roommates).
In general, to a cat, "runs away" == "prey" and "comes right up to me" == "equal and/or potential threat"
In general, to a cat, "runs away" == "prey" and "comes right up to me" == "equal and/or potential threat"