The boyfriend objection is when a girl says "I have a boyfriend", to you, and then gauges your reaction. The boyfriend may or may not actually exist. According to The Shit Test Encyclopedia, the correct translation of this phrase is, "I have Schrödinger’s boyfriend, demonstrate to me you’re high value and I'll fuck you regardless."
Chris-chan calls the boyfriend objection the, "infinitely high boyfriend factor". The phrase was introduced in:
Chris-chan: Sonichu 3, 43 S-13.
MERRIED SEINOR COMIC: Ah, he got you too, eh?
B-MANAJERK: Shut up!
DARKBIND SONICHU: Well, Chris, I have to go, but I am glad that I was able to help you in this battle!
CHRISTIAN WESTON CHANDLER: Thank you, D.B.
DARKBIND SONICHU: I’m off!
CHRISTIAN WESTON CHANDLER: Now, as for you two manajerks, the pain that you both are feeling now should be punishment enough for going against me in my quest for a boyfriend-free girl to love and trust! I do not care about your rules, either of you, or any male, other than my father and myself! But let me make it perfectly clear that in my quest, it is very hard for me to find a girl due to the infinitely-high boyfriend-factor! And I do not want to risk getting a punch in the face from a jerk! Also, since the ladies are unable to notice my person, because they mostly have shopping on their minds, I have to loudly spell it out. So, please, just leave me alone with my Love Quest!
What women mean when they say this
An unemotional "I have a BF" response can be a way of telling you to fuck off.
Although, part of her goal may be to avoid responsibility for what she's about to do, since she can think to herself, "I put up resistance by telling him I had a boyfriend, but he went ahead and seduced me anyway." It can also be a way of telling you that she wants alpha fucks with no strings attached. It can also be a way of telling you that she needs you to be discreet (so that she doesn't get a reputation as a slut).
The "I have a boyfriend" response might just be a shit-test to see if you'll have the courage to keep pursuing her. Some PUAs advocate still perusing a woman even after she explicitly rejects you. Some PUAs go even further to say an ensuing police battle after she calls the cops is another shit-test, but incelwiki does not advocate breaking the law. Just avoid someone telling you they are taken, and never talk to them again out of spite.