Sharing your Facebook password to your girlfriend, knowing that you aren't hiding secrets from one another might, at first, seem romantic. At least if you're in second year high school. If you aren't, having to share your password to something that's supposed to be your own private domain sounds like a clear lack of trust between the partners.
As tech site Gizmodo puts it, "This isn't about having something to hide—it's about keeping meaningful boundaries in an era when there are verrrrry few," and we totally agree.
If she continues to insist after explaining this, maybe you can try these convincing reasons...
1) "I respect your privacy. I hope you also respect mine."
2) "Would that make our relationship stronger?"
3) "Sige pero bahala ka sagutin pag nag-message angkan ko."
4) "It hurts to know that you don't trust me."
5) "Okay but in one condition: Beat me in basketball."
6) "Ibigay mo muna sa akin 'yung password mo."
7) "Naku babe, naka-link sa Facebook ko 'yung PayPal account ni mama baka pagalitan ako pag nalamang binigay ko sa'yo."
8) "I'm soooo sorry but according to Facebook's Terms of Service Section 4.8: You will not share your password, (or in the case of developers, your secret key), let anyone else access your account, or do anything else that might jeopardize the security of your account."