The friend eidolon system was changed with the Quetzacoatl event update. Now each friend can provide up to 6 eidolons (1 per element, chosen from the primary eidolons equipped to your 6 teams), potentially increasing the options available to players. However, eidolons in a lower-letter party (e.g., A) will mask eidolons of the same element in subsequent parties (e.g., F), even if the preferred eidolon is in your active party. Also, useless eidolons like Diabolos will just clutter the list.
Edit 10/6/2017: The latest version of the full guide can now be found in Sanahtlig's Kamihime Project Game Guide, where this guide has been collected with many others.