Hi Bruce,

I'm not really sure why is this related to Easysocial group. Where, google will generally search site that have links linked to your site (researchbreeder,com). And as the listed in your screenshot, google has found that contents in thenationaldogdirectory.com have links that linked to your site researchbreeder.com.
As example that I can find in thenationaldogdirectory page there is few links was linked(some of it I've highlighted in the screeshot) https://www.screencast.com/t/121rhPdd

The total number of actual links from TheNationalDogDirectory.com is less than 20. Why does it think there are 1875?

Can you do some further research? I have to get this figured out.

Thanks!

To be honest I'm also not really sure how googles webmaster detects the links linked to your site, it might duplicate links. But, I've do some research on the net you can further check this by download the links data into csv/googledoc file.
By the way, it is possible to provide us with your google webmaster tools access?

You can add the information needed by edit your first post in the Details section or you can just include your site's access once at http://stackideas.com/dashboard/site rather than needing to keep adding them in your replies

reference: https://www.pageonepower.com/linkarati/monitor-backlinks-google-webmaster-tools-negative-seo