On Sincerity. Sincerity stems from authenticity, authenticity from the self. The idea of being authentic to yourself implies, to me at least, that you have a set or sets of guidelines that your existence follows when it interacts with the world, and with your inner world respectively. The guidelines are not necessarily the same for the self and the interaction with the other. The differing sets of values can arise because of a variety of cultural or interpersonal reasons-say a strict childhood, oppressive regime, or anything in between.
So then there lies a problem of defining sincerity, you run the risk of becoming sort of a Cassandra, if you will-when one is sincere according to the guidelines their exterior self presents, the only one who does not believe themselves is themselves, and when one acts according to the values they may truly believe in, the people around them react with disbelief and anger. A lighter version of this phenomena may be experienced by someone who is "breaking the mold" of what they have previously done in favor of something new.
Sincerity we can then say is the act of ones inner values and external schema being in alignment with each other. It is important for the self, as unless you are amoral you will begin to build resentment of yourself. This resentment degrades you into a weaker and weaker self, and thus you will eventually lose yourself.