What similarities were there between society in renaissance italy and the ancient greek and roman civilization ?

The historical period preceding the Renaissance in Europe was the Middle Ages, which had a very strong focus on God and everything related to Jesus and soul salvation. This focus was central to the lives of every Christian. Art, as an indication of the taste, times and concerns of the people who produce it was thus almost exclusively created around religious themes.

As an unexpected  consequence of the Crusades (eleventh to thirteenth centuries A.D.), the expeditions organized by western Europeans to reconquer the Holy Land from the infidel Muslims, many Europeans got in contact with books, of all sorts of subjects, produced by the ancient Greeks and Romans which had been translated and even commented (enhanced) by the Arabs. A taste for the "classics" (ancient Greek and Roman works) gradually emerged among the Europeans in the Middle East and some even brought it back to Western Europe, especially the Genoese and the Venetian merchants. The focus of these works was mainly centered on man and all of its aspects: physical, mental, spiritual, etc. Whereas the medieval art was always solemn and excessively serious, always focused on religious themes, the art and thinking of the Renaissance took many of the values of the ancient Greek and Roman societies and granted a lot of importance to man again. The Renaissance began as an attempt to replicate (faithfully copy) the works of the Classic Antiquity in science, politics, philosophy, art (painting, sculpture, architecture), etc.

The invention of the printing press in Germany in the mid 1400s made books cheaper and easier to acquire, and contributed to the rapid spread of the forgotten ideas of the Greeks and Romans and a radical change of thinking somewhat less centered in God.