Facebook – Why does Facebook show last login of some friends and doesn’t show that in others

The number of mutual friends now includes mutual friends whose accounts have been disabled, but these friends are not displayed. Also, if the person's full list of friends is hidden to you, a mutual friend who also has their full list of friends hidden to you will not be displayed as a mutual friend.

Based on comments I know that you don't have any other devices connected (which is a big first thing to check if others have this problem in the future). And you have tried the 'traditional' turn off chat:

This is not a duplicate of How can I log out of Facebook chat?. It says “Turn off chat” on that question's answer but I say “I turned off chat but it still show me as online” — these are different issues.

Based on other reports within facebook (e.g. I am seen online even when I am offline) it seems like many others are having this problem and that it is, indeed, a bug. However, a temporary workaround that can be successfully used is to manipulate the Turn on chat option for only some friends mode.

To turn chat on for just some friends

1. Click gear in the chat sidebar
2. Select Advanced Settings
3. Click Turn on chat for only some friends
4. List the friends you want to turn on chat for

If you select just one friend to appear online for you should successfully appear offline for others.

As I mentioned in comments, here is the link through which you can report a bug with facebook chat.