It was 'dog eat dog'.

I'm not even sure what that sentence originally means. Is it supposed to be like "It's everyone for themselves"? In that case, it would mean the every person is thinking of only their own self-interests and not about taking care of other people. Everyone is being selfish.

Everyone was looking out for their own interests. No one cared about anyone else. Everyone was being selfish. Each person was just trying to get what they wanted. It was every man for himself. (a common idiom) People were only thinking about themselves. There was no sense of teamwork or cooperation.

They were looking out for themselves.

Can you explain your sentence?