<p>Good lord, what nonsense has your English teacher been telling you? Of course you can use asyndeton. Of course you can start a sentence with “but.” Obama did it multiple times in his latest inaugural address; Shakespeare did it (“But, soft! what light through yonder window breaks?”); Noam Chomsky did it in his book Syntactic Structures (and if Noam Chomsky is not “an expert in the English language,” nobody is); the New York Times does it. It is not in the least bit ungrammatical. </p>