A polite way of saying "you're honestly terrifying and I'm worried a more direct rejection will cause you to break into my house and murder me in the night."
People on the receiving end of this phrase are expected to simply grow up and take the rejection like reasonable adults instead of whining like small children over the internet.
Person A: I like you.
Person B: I'm sorry, lets just be friends.
Person A: Oh ok. I can't say I'm not disappointed, but I understand that you are under no obligation to love me even if I was kind to you and we share a lot of the same interests, and I also understand that you are not obligated to give me a reason as to why you don't like me. I'll respect your decision because I actually have respect for you, and that respect is not and never was hingent upon whether or not we would have sex.
What a girl says to you when she'd rather be with an asshole who will use her, abuse her, and eventually break her heart, even though she knows that you would never do those things to her.
When a girl says to you, "let's just be friends", that's like your mom telling you, "the dog died, but you can still keep it if you want to."
You: I love you! :)
Wench: Let's just be friends..
You: Gee thanks, couldn't you have pushed me off a two-story building, or shot me? It would have hurt less. :(
Basically the way someone will break up with you if they are trying put it nicely (see euphemism). The word "just" is the word that hurts. It's like saying, "Let's never go further than being friends. Never." Take out the "just" and it doesn't seem so bad, right?
"Hey Paul, I really like you, let's just be friends." Ehh, this doesn't work.. There has to be a "but" in there.
"Hey Paul, I really like you, but let's just be friends." Perrrfect. That one hurts more than a freight train.