I don't have an answer. I haven't paid attention to times so I didn't even notice. I have the same problem when I try to change the time zone in my profile. I noticed that if I change to 'GMT - (whatever number applies to the time zone you seek),' that seems to work. I was able to save that.
The quick fix would be:
1) Google 'What is GMT'
GMT: Greenwich Mean Time - World Time / Time in every Time Zone
2) Choose a city that applies to your location (East Coast of U.S., so NYC in my case)
3) then see how that city's time related to GMT (in the case of NYC, GMT-4:00)
4) Change time zone in your profile to that. My change was saved when I did that. I don't know if it works with all choices.