"The cat is drinking milk and I am paying."
Translation:Die Katze trinkt Milch und ich bezahle.
In a main clause, the verb comes in the second position. (Unless it's a yes–no question or a command.)
In a subordinate clause, the verb comes at the end of the clause.
Here, there are two main clauses: die Katze trinkt Milch / ich bezahle.
Each of those two main clauses has the verb in the second position, after their respective subjects die Katze and ich.
Those two main clauses are joined together with the coordinating conjunction und, which doesn't cause any word order change in the two clauses that it joins.
Since I don't see a reply, I'll give a possible guess: 1) The “normal“ German for “the cat“ is “die Katze“. The “normal“ word for “the tomcat“ is “der Kater“. Two different words -- maybe that's why. BTW: “der Kater“ is also the word for “hangover“! ;-) OR: 2) Maybe you didn't capitalize the words “Kater“ and “Milk“. I'm just guessing why Duo rejected you. You're obviously a good student!