A web page with Javascript can see & send off something you paste into a text box as soon as it appears. So if you accidentally paste some confidential information, like a password, that's a security hole even if you notice and delete it straight away. This happens even for totally innocent reasons, like search-as-you-type.
Ctrl-C/Ctrl-V copy and paste is not such a big issue because far more people are familiar with it, and it requires more deliberate actions on both sides (copying and pasting). So you're less likely to accidentally copy something around that you didn't mean to.