Some people aren't cut out for it. I've been in the same position as you and couldn't understand why girlfriends didn't get enthusiastic about doing the same sports as me.
It always ended up the same way. I'd convince them that they were missing out and that it was easy/fun, they'd get scared, put off and never try it again.
I was completely in the wrong.
You shouldn't put pressure on her, imagine how you'd feel if she did it then something happened to her.
It has to be her decision.