How to remove a person from the friends list in Messenger

Method 1: 

If your case is "You choose not speak to this person over Facebook messenger", or " He or she must not be able to ping you there", you can block the contact directly from the messenger. Open the app, use the third tab, tap the extreme rightside option button for the Facebook contact and there you will find the blocking option.

If your case is, you don't want the user to see you online, then I don't think you can achieve the same from app. Probably in the desktop version you will get the option where you remain offline to a particular user, even though you are being shown online for other people in your friend list.

Method 2:

Try 'Clear Data' and 'Clear Cache' by selecting the app from "Manage Applications" list in the settings.
If no luck when all the data of your messenger is reloaded, try uninstalling then re-installing the app.