If the request were to be granted to remove what is on the other person's Facebook page, first of all, the requester would have to demonstrate that the information is inaccurate. If the source of that information is what the first person had just put up, that would be pretty difficult.
The first requirement is to prove inaccuracy or incompleteness, or that it's not up to date. Let's assume that 10 years have gone by between the original posting and the second posting and the first individual now claims that the information is no longer up to date and current. Then it's more possible. Then the organization would have to distinguish the facts. Are they still accurate in the opinion of the second person? If there's a question of opinion by the second person, then that should not lead to the takedown of that opinion of the second person.