Most people consider their friends to be more positive than themselves, exhibiting a Sentiment Paradox. Psychology research attributes this paradox to human cognition bias. With the goal to understand this phenomenon, we study sentiment paradoxes in social networks. Our work shows that social connections (friends, followees, or followers) of users are indeed (not just illusively) more positive than the users themselves. This is mostly due to positive users having more friends. We identify five sentiment paradoxes at different network levels ranging from triads to large-scale communities. Empirical and theoretical evidence are provided to validate the existence of such sentiment paradoxes. By investigating the relationships between the sentiment paradox and other well-developed network paradoxes, i.e., friendship paradox and activity paradox, we find that user sentiments are positively correlated to their number of friends but rarely to their social activity. Finally, we demonstrate how sentiment paradoxes can be used to predict user sentiments.