Peacocks - What's the Difference?

A friend has a peacock in their back yard, and this is turning into a bit of a debate. A a let the peacock hang out, or bring over her brother's dog to encourage polly the peacock to relocate to another shady back yard. So first of all, a peacocks, by definition, are not polly. That would be a p hen. She sent me a picture. This is a peacock, so let's start with that. Just the misnaming is bothering mins. It's terrible. But also, this is me, why? Like, in the last three minutes of this, i guess, why would you ever want the peacock