Without more details such as the country of ticket origin, country where card issuer (bank) is located, country where you are resident, and card currency, it is hard to answer your question.
Suffice it to say that if you have been asked to produce the card, it is because your purchase has tripped BA's anti-fraud or anti-AML systems and part of verifying that the passenger really is you is for you to show the card. BA most assuredly will deny you boarding without proper verification.
It would help immensely if you provided some detail as this may be very rare or not depending on the circumstances.