I had somewhat different experiences. For a few past weeks, the site kept telling me I had to enable cookies, which were enabled. Different browsers, a different account and a different PC, always the same problem. Strangely, a few days ago, I did get the message to reset my password, even though the same error message had appeared.
I would like to know if there were ways to avoid that in the future.
I received the same message, in my case the problem was that the 'Current Password' was incorrect.
I didn't known the current password was different from what I though it was because I had enabled the option 'Remember me for next time' and did not need to enter the password.
After using the 'Forgot your password?' option to get a new password I was able to change it.
So if you are also using the 'Remember me for next time' option, try signing out and in again to see if you have the correct current password. If not than request a new one and change it.