Imagine you keep all your life savings in a safe. Normally you take some money out and go and pay for things. But this one time, instead of asking your money, the shop owner points at a guy by the door and says, "see that guy? Please give him the key to your safe. He'll open your safe, take the amount you owe for your purchases, and deliver it to us."
Who is this guy, you wonder? You've never seen him before.
"Oh, don't worry, we're totally safe! I've done this a number of times before and nobody has ever had any money go missing. Also, check out my SafeBuy logos, don't they make you feel safe already?"
Would you give him the key to your safe?
Some hyperbole aside, this is essentially what Austrian Airlines have asked me to do. They pointed me to sofort.com, who, to my utter disbelief, requested me to enter my online banking password into their site. Just like that. Hang on, wait, did this just really happen? Maybe that was a fake Austrian Airlines site, that directed me to some phishing operation? No? It wasn't? Huuuuuuuuh?... Is this for real?!?!?!....