I think firstly stuff may need to be clarified a bit when it comes to Household Accounts, F&F lists, and Travel Companion lists. They are three distinct things.

HHA
This is where you join up members of the same household in order to pool avios, this isn't what the OP is talking about. I assume the OP isn't in a HHA, but if they are it would be useful to know.

F&F list
Everyone has this although for some they may never have added anyone, it is a list of up to 5 people. If nominating someone for a partner card they need to me one of the people in your F&F list, Also if you have a HHA one of the restrictions is you can only book reward flights for someone either in your HHA or in your F&F list, if you are not in a HHA you can book reward flights for anyone - they do not have to be in your F&F list or even your Travel Companions list, you can book for whoever you want.

Travel companions list
As Globaliser notes this is just a list where peoples details are saved if you have booked for them in the past, nothing more. When you go to book a reward ticket the drop down list will include both those on your F&F list and those on your Travel Companions list - if you select any of them it will populate the passenger name and exec number fields. You are also free to book for anyone else, it specifically says "You can select a passenger from the drop-down list below or enter a new passenger's details directly into the fields."


Going back to the OP's issue, the F&F list is the relevant one for partner card nominations. You shouldn't have been adding people in to it simply to book reward flights, there awns;t any need to do that and the Travel Companions list would have worked. You can add people to your F&F list when you want if there are free spaces. However, as noted by Globaliser, unfortunately once your F&F list is full you can't simply remove people at will, as noted on ba.com:

So once your list is full that's locked for 6 months and you can't remove anyone to add someone else in to one of the 5 slots until the 6 month period has passed.

The agent is right in the sense that the F&F list was brought in to allow those in a HHA to book reward flights beyond HHA members - I think this was introduced around 2014/2015. Before if you were in a HHA you could only book reward flights for those in the HHA and no one else. If the F&F allowed completely free addition and removal it really would be a pointless restriction. However, as the GGL partner cards also work from the F&F list this restriction clearly has an impact on that too.