Why do all inter-halogen compounds contain an even number of atoms? Why do all inter-halogen compounds contain an even number of atoms?

All halogens have one electron in their valence shell. One covalent bond is formed by 2 halogen atoms (sharing one electron each). If in the compound an odd number of atoms were involved, then an odd electron compound (unstable) would be formed. IF4 would contain 1 lone pair and 1 odd electron, hence unfavorable. 

Is my answer correct? If you have any better explanation, please share it.
Yes neutral $\ce{IF4}$ would be unstable because it would have one lone pair and one unpaired electron.  The extra lone pair is not a problem because Iodine is large enough to exceed an octet, but the unpaired electron makes it a free radical.