We're our own worst "enemy" or "enemies"?

Technically you're right, but this is one of those irregular things in English as we speak it.

The 'We' in 'we are our own worst enemy' is a collective noun. It's like saying 'Iran is our worst enemy' (which it's not, I'm just using it as an example.) Iran is a country, but the word also means 'the Iranian people'.

You know if you talk about 'the American people', it's a plural. The American people are, not the American people is. But you can also say 'all the peoples of the world', in which case 'peoples' is a plural of individual 'people'. So you could say 'Nearly all the peoples of the world agree on human rights, but one people disagrees'. (Hope I'm not confusing you.)

Anyway, when we talk about ourselves, -us-, being our own worst enemy, we're talking about a single enemy.

We're our own worst enemies. is grammatically correct sentence.

We're our own worst enemy is the correct term. Mainly because the "we" refers to A group of people, eg people who don't or won't stand up for themselves when bullied, etc. We are our own worst enemy.

It would be correct either way.

You are correct the "we" is plural and therefore that enemies should be plural, but keep in mind that the phrase "the enemy" can also refer to a group of people and not just one person.

there is a set rule and it should be plural, but in non-oxford english we would really say it either way, so in my mind, neither is right, the plural version is just more right, but in english you can refer to a group of people or an "all" as an "it" or singular and it would not neccesarily be seen as wrong. it is enemies if we individually are our own worst enemy. but if the world population collectively is everyones worst enemy. then it would be enemy.