Honestly I can't think of a legitimate reason why anyone would need another person's password unless there was an emergency of some kind. I have never had a password on my cell phone. As for having one's email password that is equivalent to having someone open up your snail mail in my opinon.
Facebook and Twitter are social media and anyone who is a "friend" or "follower" can see most of what you post. Naturally if your relationship status has changed that might raise some eyebrows. Lastly their is a big difference between a "significant other" and a spouse. The typical young single person may date a new person once a year or every other year if not more often. Having to start every new relationship with the exchange of passwords and then changing them after each breakup would get old. An unhappy ex can do some serious damage to your world with passwords,debit card #s...etc