I think it may be worth explaining the group 7 ‘reactivity trend’.
Note that ‘halogen’ refers to a group 7 element and ‘halide’ refers to a salt formed in which the group 7 element forms a monatomic (single-atomed) anion with a charge of -1.
Going down the group, the halogen atoms get bigger and they have more electrons. This makes it harder for the halogens lower down the group to gain electrons and harder for the corresponding halides lower down the group to hold onto their extra electrons. These observations are both because the bigger the atom/ion is, the further the negative electrons are from the positive nucleus (hence the attraction is weaker) and the more electrons the atom/ion has, the greater the ‘shielding effect’ (repulsion against the outer electrons) is, which makes picking up and holding onto an electron harder.
So what this results in is the halogens towards the top of the group being good at displacing the halides of the group 7 elements at the bottom of the group.
Ignoring astatine and astatide ions:
F2 can displace any other halide (Cl^-, Br^- and I^-) and F^- cannot be displaced by any halogen.
Cl2 can displace Br^- and I^- ions and Cl^- can only be displaced by F2
Br2 can only displace I^- ions and Br^- can be displaced by F2 and Cl2
I2 cannot displace any other halide ions, but I^- can be displaced by F2, Cl2 and Br2