Is your advisor allowed to read your emails?
What is the method of the email access?  If it is provided through the university or accessed on a university-provided computer, then it may be the case that they have a legal right to those contents.  This was the case at at least one of my workplaces in the USA.  If you are using your own email address, and your own computer, then I don't see how they could have the rights to access it.

Either way, it is best to have a separate email for all personal/private communication rather than risk it on your school email.