DNA Testing: Ex-Girlfriend Wants Me to Sign Rights Over if Paternity Test is Positive

My question involves paternity law for the State of: Canada

So my ex has a child that is currently 6 years old. We had 'relations' in the months leading up to her pregnancy, but she also started dating another guy around the same time. Anyways she raised the child with that guy, even putting his last name on the birth certificate. So of course I didn't think it was mine. However, now after all of these years she wants me to do a paternity test. I agreed to it but now she is saying that if it is positive, she wants me to sign my rights over. I know what that means but I don't know why she is asking that. Why would she even talk about that before we determine if I am the biological father or not? I find this odd and think she is up to something. I don't think it is a child support thing because she hasn't asked me for anything at all up until now, so what else could she be trying to do? What kind of mother would want the father out of the picture before the paternity test is even done?

I don't want to do it (give up rights) but she said she will take me to court for it if I don't sign them over. I am a student and can't afford a good lawyer at the moment so I don't know what to do. Any advice will be greatly appreciated.