The conflict between Laocoon and the Trojans was that when
the Trojans saw the Greek ships leaving, they thought the war was over.  When they saw the wooden horse, they thought
it was a gift and wanted to bring it inside Troy.  Laocoon objected thinking it was a trick but
the Trojans disregarded his warning. 
Laocoon insisted but Athena had two serpents from the sea attack him and
this enabled the Greeks to sneak in and conquer Troy.
 
        
             
        
        
        
The faulty logic that the given sentence contains is B. Either-or Fallacy. An either-or fallacy is the limiting of possible answers into two or it is oversimplifying. In the given sentence above, it only gives two possible answers: either meeting the deadline, or if not the town will suffer.