Read this.Sorry that is all!
Let's assume she thinks it's too dangerous. What she needs to understand is it is more dangerous not to cycle. The health benefits outweigh the risks; that is cyclists will live longer on average than non cyclist.
The problem is, that is not immediately apparent. If you are an unfortunate victim of a RTC, she will wish you hadn't cycled. But if you get a stroke at age 68, nobody will think "if only he'd taken up cycling 30 years ago".