Should I explain why I don't want to add someone as a friend on Facebook?

Just ignore their "friend" request. If you don't want to connect with them, then don't try explaining why - because you will need to connect with them to just do that. Nobody needs to be humiliated just for trying to get in touch with someone they thought of as an old friend or acquaintence. If you don't answer at all, it will be better than answering just long enough to say "I have no interest in reconnecting with you". If the past is truly the past in your mind, then just don't respond to them at all.