My girlfriend is making me choose between facebook or her ?

she just called me saying i have to choose to be with her or facebook sounds funny, but thats what she said i just clicked on her. just because i changed my password so she wont be on mines. i got mad because she has my account on her PHONE and i think thats some stocker shh. so she gets mad because i did it. she thinks i have something to hide, because she cought me looking at other girls. i have never talk to no girl over Facebook nor ever cheated on her. but she thinks i will. we've been together for 3 years. i dont care if she has my password, ans checks it onces in a while when she bored, but to be on it all the time is too much. what you guys think? i dont want to close my Facebook just because she said so. im not going to live my life with a girl thats so pushy, im the man "of the house" so to speak