Ah, yes, you had not made things personal for a while, I was sort of missing it!
You always do the same thing, it's sort of funny:
step 1: someone makes a point ('BAEC is a frequent flyer programme') which many people might intuitively agree with;
step 2: for reasons that belong to you (unlike you, I won't try to double guess them), you do not agree with that. You think that because BAEC members can also accrue based on shopping, hotel stays, car rental, credit cards, banking, etc, it does not qualify as a Frequent Flyer Programme. Fine, totally your right to disagree. You include bits of BA prose that explain every way in which you can accrue avios as supporting your argument, which is again perfectly fine, and make two odd accusations: 1) that seeing BAEC as an FFP is 'outdated' (not sure why really, the exact same argument that you are making now could have been made in the exact same way 15 years ago when the same earning opportunities existed, so if seeing BAEC as an FFP is wrong, then it is entirely wrong and has been for a long time, not just outdated), and that 2) seeing BAEC as a Frequent Flyer Programme is, in some bizarre way, 'inequitable'.
step 3: person says that they disagree with you. Yes of course, all FFPs allow a variety of sources of accrual, but it does not mean that they are not Frequent Flyer Programmes. In answer to your point that there are plenty of ways to accrue, person answers: 'sure, but then in terms of status, it is only based of flying, ergo, 'flying' and 'shopping' are not considered equal by the airline (note, for example, that some other FFPs count credit card use and purchases towards status, BAEC does not), and in response to your quoting bits where BA does not mention BAEC as a frequent flyer programme, person says that BA do in other places such as their own booking system (not to mention others') as well as their own booking records. Again, you are free to disagree but I'm afraid I don't 'have' to be convinced by your argument to play fair.
step 4: you not-so-subtly distort what the other person is saying (I said 'BAEC is a Frequent Flyer Programme', you claim that I said 'BA is a programme for frequent flyers' which is entirely different).
step 5: you hint at a dirty suspicion of necessary bias from those who do not agree with you and personalise things ('I wonder why it is so important for you...'). Well, it is not, I just don't agree with you that BAEC is not a Frequent Flyer Programme. I couldn't care less if it were a frequent embroidering programme, a frequent soup making programme or a frequent marathon running programme. I just substantively disagree with you that the fact that there are plenty of ways to accrue means that it is not a Frequent Flyer Programme, and in fact, its logical conclusion which would be that there are hardly any Frequent Flyer Programmes left on this planet since virtually all allow for plenty of non-flight accruing options. And as a consequence, it does not seem illogical to me that the amount of flying ones does will have an impact on how people will be treated by the airline which owns the FFP. My point is not normative (it is not 'good' or 'bad' - you are the one talking of equity and the likes), it is descriptive. Perhaps you could consider the possibility that even if you are absolutely persuaded that you are always right and those who disagree with you are always wrong, which is perfectly fine by me, those annoying people who have different opinions from you might do so without necessary being motivated by some dark and dodgy motive.
So by all means, continue thinking that BA Executive club is not a Frequent Flyer Programme, but kindly leave me out of it.