Turn out to be single everytime when fighting with a girlfriend/boyfriend.
It doesn't really mean you change your relationship status to be single. It's kind of sarcastic. You might be feeling angry, unhappy or sick of it.
ทะเลาะ is one word. Do not separate it. It means to fight or argue.
It is always followed by กับ which means with. So it would be ทะเลาะกับ (to fight or argue with).