Do we really choose our parents before we are born?

Yes, you do.

Prior to your current incarnation, you settled on a particular theme for your next life. You then chose fellow souls to be the major actors in your next incarnation, including your own parents.  Soul plans are always a collaborative relationship; the other souls also have their own themes to explore, for which you are doing them a service in kind through your interaction with them. Your chosen parents would provide you with the early growth experiences and scenarios that set the stage during your early years.