Ignoring user password on signup

I had trouble logging in with the password I created at signup.

This is the signup form:

On signup, user is asked for her desired password (twice) and it is even validated, throwing an error if left blank. However, upon submit, a password is generated and displayed by the system. The generated password is the one that works, even though the welcome email says the password is [user set].

Ideally, I would keep the user defined password and loose the activation email. (As I had it before). Can anyone tell me how to get there from where I am? Please be explicit, Im a newbie.

Thanks for your great support