"I am thirsty."
Translation:Ich habe Durst.
No, read again.
"Der Durst" is "the thirst".
So "ich bin Durst" translates to the non-sensical "I am thirst".
"I am thirsty" would literally be "ich bin durstig".
But the fact is that while English speakers do say "I am thirsty", German speakers (and lots of others, for instance the French), say "I have thirst".
Different people, different habits. If you try to translate word for word, or bring things typical from language to another, you'll never sound natural, nor really understand others.