Hello Eganlynn! Thank you for participating in the Apple Support Communities.
We understand that you’re unable to migrate your information from your old Mac to your new Mac because the security code isn’t appearing to authenticate both Macs together. We'd like to look into this with you to see how we can help.
Great thinking to try the steps outlined in Move your content to a new Mac to resolve this issue.
Are both devices up to date with the latest macOS available to them? Update macOS on Mac
As stated in the article, “Install all available software updates on both computers. If your old Mac isn't using OS X Lion or later, and your new Mac isn't using OS X Mavericks or later, follow the Mountain Lion migration steps instead.” You can find those steps here: How to move data to your new Mac using Mountain Lion and earlier
Make it a great day!