Private e-mail accounts

[Krielke]

I made a few e-mail accounts in my CPanel, secured with a password. When I open webmail in my CPanel by Horde, I can see all the e-mailaccounts I've made and I can open them all. There's never been asked to write down the password.
My purpose is to protect the different mailadresses, so that 'personA@myname.com' cannot read the mail for 'personB@myname.com.
How can I make this work?

Thanks!!!