Why does making myself invisible log me into Messenger?

Today I noticed that when I logged into Yahoo Mail and went to my Inbox, I was receiving instant messages from someone I didn't know. I also noticed that I had been logged into Yahoo Messenger without permission. So I logged out of Messenger. Then I went into the "Hi, User" options menu in the upper left of the display and clicked on Invisible to Everyone.

As soon as I did this, I was logged back into Messenger without permission and started receiving those unwanted messages again. Guess I wasn't so invisible after all.

I want nothing to do with Messenger. I don't want to be automatically logged into Messenger when I log into Yahoo Mail and I don't want to be logged into Messenger when I select "Invisible to Everyone" in that "Hi, User" options menu.

I looked through the mail and profile settings. There is a Messenger settings menu but does not include the option to disable it entirely. Likewise, there is nothing in the Mail settings or Profile settings (not even in the Privacy section) that includes the option to get rid of Messenger entirely.

Is there a way to do that besides logging off every time it arbitrarily logs me on?