There doesn't seem to be any mystery surrounding it. By all accounts it was an incredibly uncomfortable experience for everyone involved. Elvis didn't have the slightest interest in being personable and forthcoming with them, and because the meeting took place in his home, the members of The Beatles didn't know how to handle it except to show off that British politeness. But it was extremely awkward, they weren't able to lighten the mood, so they took their leave of him. The biggest question is: "If Elvis didn't have any interest in hosting them, why did he agree to have them over in the first place?" They've never understood it, and he himself never offered an explanation for it.