Why do I need to use a personal Facebook account?

TLDR? This is the way Facebook verifies you for security purposes.

The connection to Instagram Business account is through your personal Facebook account - Instagram (which is owned by Facebook) now requires that we create a connection to the Instagram Business account through a Facebook account, which is an administrator of the Facebook page to which the Instagram Business account is associated. 

We only use the connection to access the Instagram Business posts, nothing else. We cannot see your posts or personal information beyond your name.

So you'll need to go to the Account Connections page and Add an Instagram Business connection. 

It'll show your personal Facebook account name next to the connection.