My girlfriend has been nagging me to remove the password from my phone. 
I have nothing to hide, but 
I don’t want to. Should I?

The weirder you react, the more suspicious you’ll seem. As long as you’re not up to anything that warrants hiding, you’re entitled to your privacy. There 
are so many reasons to have a password – mostly for security. (Have a laugh with her about wanting to make sure “those” pictures remain private.) If she doesn’t get the joke, then you two probably have trust issues. Ask her why it’s a problem, and then, without belittling her concerns, explain how important mutual trust is to you. If she still refuses to loosen up on her no-password policy, consider it a bad omen.