How do I log out from Steam?

Title says it all. I'm facing a silly issue.

My friend and I were talking through Discord and we randomly decided to play CoW again. I found the game on Steam, downloaded it and informed him that the game is available on Steam.

He said ''Does it support Google login?''

and I replied 'I dunno, there is no Google or Facebook logo.''

Then he suggested me to try for him instead by using his nickname. I logged in and told him it works, you can download it throught Steam too, since we play on Steam a lot. But then I realized I can't actually log out.

I Googled it, nothing credible came up. I deleted the game from Steam, removed it from my account even, but everytime I open the game his profile automatically logs in. We also tried changing passwords.

How can we fix this issue? Our both accounts had 1 year premium too.