realsocialskills answered:

No, it isn’t. People in a relationship are still two separate people. Some people are ok with sharing passwords with their partners, and some aren’t. It’s not something it’s ok to demand.

Some reasons not to share passwords:

• A computer is a very, very personal thing for some people. It can effectively be an extension of your mind and body.
• It’s ok not to want to share that in an unbounded way.
• Or, in other words: A computer (or a cloud account) can be functionally an extension of your brain, and you don’t actually have to give your partner the ability to read your mind

Also, your correspondence can involve other people’s confidences:

• Sometimes, friends need to be able to tell you things without that being effectively the same as telling your boyfriend
• Likewise coworkers
• Likewise students if you’re teaching
• Especially if you are in a profession where people often tell you deeply personal things with an expectation of confidentiality

It’s ok not to want to share passwords, and it’s a red flag if someone is demanding it. (Particularly if you’re not at the point of living together, and especially if you’re young. If you are a teenager, no one but you should know the password to your email account and other things that are similarly private.)