"I have to stop drinking beer."
Translation:Bira içmeyi bırakmalıyım.
I can't possibly stop someone else's drinking. (I can stop by force, but the Turkish sentence has the verb 'bırakmak', which means to set aside, to leave) So there's no point in further specifying who does the drinking. It's like saying: I have to stop my drinking beer.
Malı and Meli are the 'have to' but as suggestion. ''Beklemelisin'' for example it means ''you have to wait'', but it's coming as suggestion as the English ''should''. İ would 100% use ''Bira içmeyi bırakmam lâzım'' here, which is also what İ wrote and got rejected by Duolingo...