YOU SAID:
an old man eats chicken that is me and I eat him
INTO JAPANESE
老人は私である鶏肉を食べ、私は彼を食べる
BACK INTO ENGLISH
The old man eats chicken which is me, and I eat him
INTO JAPANESE
その老人は私である鶏肉を食べ、私は彼を食べる
BACK INTO ENGLISH
The old man eats chicken which is me, and I eat him
That didn't even make that much sense in English.