Many employers like CS degrees, but then again many don't place much importance on it. Use that to your advantage during your journey to a degree (which is really for YOUR sake, not theirs).
You're going to come into conflict with your parent regardless, so it's better to do it on your own terms and prepare them for the life you intend to live. They love you and will eventually come around, even if it's going to be painful and stressful in the interim.