Talk to them openly and honestly. I would ask them what they fear and why. If you listen to their fears your answer should lie within that. You have to get them to minimize their fear or apprehension. The only way to do that is to get them to open up about it and then address it. My wife's brother died in a motorcycle accident. She was not happy when I approached her about riding a road bike. She has never minded my mtb riding but in her mind this was different. I had to listen to her to figure out how to address her fear.
As a parent, I understand that fear but am open to discussion. If you resort to telling them what you want and why, you will probably not get them to move on the subject. Get them to open up and then start with your sales pitch.