When my cat first came into my house I was a little mean, and I dont know how to make her love me?

I never like kicked her, but things, and right now she doesnt love me, and we leave her in the basement everyday but bring her out after we come home,or else she will go on the table, how can I get my parents to say " we can trust her (AKA my cat). So what is the point of having a pet that does not love you I mean "come on !!!" What I mean is she doesnt pur, or come to me, I have to come to her, if I pet her she walks away, if I sit by her she walks away. So should I stay away from her, but for how long? I need to know how to get her to love me, how to get her to come to me when I'am just sitting down minding my own business, how to make her pur, how to make her love (me). I need to know, I'am desperate, I need help. So if anyone knows please tell me what to do to get my cat to love me, pur, be with me.