This can be caused by the launcher itself not updating this is how I fixed it after realizing that was the problem.
go to Documents\My Games\FINAL FANTASY XIV - A Realm Reborn\ open up FFXIV_BOOT.cfg in word pad or notepad.
you should see this
<FINAL FANTASY XIV Boot Config File>
<Version>
Version 2
Language 1
Region 2
EulaAgreement 1
StartupCompleted 1
B4EulaAgreement 1
BootVersionCheckMode 0
ConfigReset 0
the line in bold is the key change the 0 to a 1 and it forces it to check version upon opening the launcher.
After doing this it updated launcher and the game fine.