The correct answer is option 1: "It is an inter-governmental body within the United Nations system made up of all members of the UN." This statement is not correct. The Human Rights Council is not made up of all members of the UN. Instead, it is composed of 47 UN Member States, which are elected by the UN General Assembly. This means that not all UN member states participate in the Human Rights Council.

Option 2, which states that the Human Rights Council is responsible for the promotion and protection of all human rights around the globe, is correct. The primary purpose of the Human Rights Council is to address and address human rights issues globally.

Option 3 is also correct. The United Nations Commission on Human Rights was replaced by the Human Rights Council. The change was made to improve the effectiveness and efficiency of the UN`s human rights mechanisms.

In summary, the incorrect statement is option 1, which suggests that all members of the UN are part of the Human Rights Council.