Y'all know you can block a person without deleting your own FB, right?
According to HELP on FB, there are two ways:
1) Settings>Privacy Settings>Block List>Type the person's name or email. It'll give you a search result. Find the correct person, and click Block.
2) Go to the person's profile, at the bottom click 'Report/Block this Person' and in the popup, check 'Block' then hit 'Submit'.