MY girlfriend is emailing other guys saying "i belong to you" and etc... am i stupid?

MY girlfriend is emailing other guys and flirt with them over the internet. I caught her installing a key logger on her laptop. She says she does this kind of things when she has an arguement or fight with me. She says she feels safer when she talks to them. The reason for that is i beaten her few times. I dont regret any of the beatings( when i say beating is holding her neck grasp her arm and all that...) except for ONE( i kicked her but and hit her face)..She knows i am not happy but she is still emaling them facebook them although i stopped being violent.We want to leave each other and break up sometimes but we cant because we love each other.Sometimes i tell her to leave the house and dont come back but i keep her passport with me so she cant leave US.When i give her passport she does not leave and stay with me. She always say i am not handsome , i come from the slum, i am not smart and etc. she rarerly tells me good words. but she is still with me. whats going on with us any suggestion? Normally i should break up with her after i found she is writing to other guys but i couldnt. i really dont know why i cant or couldnt. Am i stupid?