I see why you are confused - let me explain.
Every company - aviation or not - has a culture. There is not such thing as absolutely subjective recruitment - no such thing as simply selecting those with the best grades. It comes down to impressions made on the day, and ability to gel with those interviewing you. This is not isolated to BA alone, but is common across all businesses (at least those in a position to choose).
BA has, what it believes, a honed training system that has been developed from years of experience. Others have other systems, that differ in many respects. What they want therefore are people that fit that training system and culture.
So long as you are not one of the starry-eyed people focussed only on BA, you should not be offended by this. It is pragmatic, suits some people, and won't suit others. An organisation tends to be set in its ways - if you don't agree, a one-man army to change it is hardly conducive to a positive working environment.
Integrated v modular in BA is somewhat developed from the self-selection argument. Self-selection is not thought positive, both in BA and many other airlines - not for the reason that modular students can't handle it (many can) or that they will never recruit them (they have), but that the likelihood of success on an intense type-rating was demonstrated (a number of years ago) to be significantly lower. With the ability to choose whomever they liked, their preference remained for integrated students - the supply was there (and they of course knew the exact product, having developed it with BAe at Prestwick - now Jerez, and working with Hamble / Oxford / Cabair students in the past as well).
Of course, this does not apply if coming from another airline with experience.
They don't like piecemeal training, lack of continuity, and any possibility that retraining will be required in the sim / on the line. Hence, high preference for integrated people who have planned a continuous training course at one location, where their records are available, with a known quality product. Hence, why they don't like people who are starry eyed, train at each stage as and when they can afford it, and bet the ranch on the less safe option (in their eyes).
The business itself is quite frankly a palava as well. They need people who can deal with waiting 20 years for command, a disaster of an operation at Heathrow, and operating at a high level with premium customers.
It is one of many companies in the UK, but one that employs just a huge number of pilots.
The question is - do you prepare yourself for any eventuality, and be in a position to step into a business that controls half (the present - perhaps not the future) of UK pilot jobs, or turn your back on that segment entirely.
Does the culture fit - RAF types, old sponsored types, recruits from other airlines - many who were modular, tours, longhaul, shorthaul. Or do you prefer to be at home every night with easyJet?
Suits some, not others - they need to match people to that operation, and in the simple fact of selecting people and rejecting others, that is not arrogance in itself, but simply a measure that they can indeed pick and choose.