How can I convince my parents!!!?

[Qwerty]

she has obviously heard this information, presented as a fact somewhere, (probably CNN or FOX news) and is unwilling to listen to anything different. the truth is that using credit cards on the internet does have its risks. if you had malware/virus on your computer, or the site that you used the card at was compromised, then that info could be harvested and sold or used illegally. however, online transactions are probably as secure as they have ever been. 99.9% of sites use encrypted connections when processing sensitive information and take preventative measures to ensure that customer data is unreadable, even in the event that they are compromised. use a good password when making the account (a new original password....not "monkey" for example).
the truth is that her card info is entered into a computer at some company as she gives it out over the phone anyway, making it as vulnerable as if it was entered into a site.
just remember, the more you try to convince her or use jargon to explain why it is safe, she will stop listening more. maybe she would listen to this (or another persons) answer?