It could be that "pessimist" and "faultfinder" are both correct, but one is more correct than the other. It's a tricky question. Even though "faultfinder" is less commonly used in conversation, it can be the more correct answer in the particular sentence they gave you.
It's helpful to look at the definition of each word and see how they are linked.
"Cynic" is: a person who believes that people are motivated purely by self-interest rather than acting for honourable or unselfish reasons.
While a pessimist is: a person who tends to see the worst aspect of things or believe that the worst will happen.
A faultfinder is: a person who habitually finds fault, complains, or objects, especially in a petty way.
In this case, the cynics are immediately criticising the pledges and finding fault in the lack of self sacrifice, therefore "faultfinder" can be the more correct answer.