Is it okay for my Fiance to demand to see my emails?

I've been in a Masters program for the past 2 months and it's been taking over my time entirely. I regularly communicate with my classmates about the class, and more often now since we have an exam coming up really soon. My Fiance walked in on me emailing a classmate (Male) the other night and demanded to see the email. After I regularly assured him that he was overreacting and that there was nothing but school being discussed, he still stood over me and continually requested to see the email. After I wasn't giving in, he literally snatched the phone up from the bed and walked out of the room to read it. I tried to get my phone from him, but he wouldn't let me. By the way, there is absolutely positively nothing that I have been hiding from him.