Romeo and Juliet was written by William Shakespeare sometime between 1591 and 1596 and the characters appear to be historically situated in this era. In this Renaissance/Early Modern period, the relationships between parents and their children were quite different from ours today.
Firstly, infant mortality was much higher than today, meaning that one in every three or four children died before the age of 15. Some historians believe that this made parents more reluctant to love their children, for fear that they would die soon.
Secondly, it was very common for people to have servants at home and for parents to send their children to train or work in other people's houses. Separation at an early age, then, was fairly common between parents and their children.
Finally, children were, in general, considered more of a financial burden than an asset. This may have created some feelings of resentment between parents and children during times of economic hardship, like a famine caused by poor harvest.