Back in the Renaissance, families were intricately linked with honor. "All members of a noble family shared in its reputation, good, or bad, and all relatives suffered if the family lost its honor," (Grendler, The Renaissance). Thus, members of a family would often try to maintain and bolster the reputation of whatever family they belonged to, since they had a personal interest in their family's honor. In a situation like this, even the most distantly related members, and even serving men, would try to uphold the family honor, causing a great divide between feuding families, such as the Capulets and the Montagues.
Within the play, the Capulets and the Montagues are entrenched in a violent, long-standing feud that polarizes each family against the other. Even the most distantly related characters hated the other family, as shown when Sampson and Gregory show their disdain for the Montagues in Act I, with Sampson declaring that "A dog of [the Montagues] shall move me to stand; I will take the wall of any man or maid of Montague's." (Romeo and Juliet, Act 1.1). This implies that he believes himself, of the Capulets, to be above the Montagues - a clear show of familial pride. This pride then leads to some major conflicts where neither family will back down, including the resulting fight after Sampson made that remark. It also manifests itself within the strong familial identities that keep Romeo and Juliet from making their relationship public. Juliet makes that abundantly clear when she hopes for Romeo to "Deny thy father and refuse thy name Or, if thou wilt not, be but sworn my love, And I'll no longer be a Capulet." (Romeo and Juliet, Act 2.2). This divide of familial identities and honor separates the two lovers, causing the major conflict of the play. Again, we see pride and honor (between the families, in this case) causing the conflict in Romeo and Juliet. .
A second example of the problems caused by pride would be the arranged marriage between Juliet and Paris.