We consider a simple model of agents modifying their opinion about themselves and about the others during random pair interactions. Two unexpected patterns emerge: (1) without gossips, starting from zero, agents' opinions tend to grow and stabilize on average at a positive value; (2) when introducing gossips, this pattern is inverted; the opinions tend to decrease and stabilize on average at a negative value. We show that these patterns can be explained by the relative influence of a positive bias on self-opinions and of a negative bias on opinions about others. Without gossips, the positive bias on self-opinions dominates, leading to a positive average opinion. Gossips increase the negative bias about others, which can dominate the positive bias on self-opinions, leading to a negative average opinion.