I am of the alarming and insufferable opinion that the Renaissance begins on April 26, 1336 with
Petrarch's attaining the summit of Mont Ventoux.
With the opening chords of
Also Spracht Zarathustra booming down the valleys, I trust.
I'd be inclined to say the Renaissance probably started when someone in France translated a book of Roman or Greek learning that the Moors had kept, and first showed above water in the 13th century with the Schoolmen, Abelard, Albertus Magnus, Aquinas, R. Bacon, Duns Scotus, Ockham, all those dudes a century earlier on whose shoulders Francesco stood.
Petrarch effectively makes humanity (i.e. "the human soul") the source of all value in this world.
Then he'd likely been reading Peter Abelard's work. Abelard was following a strand of Christian thinking about humans being made in God's image, and the what-we'd-now-call humanist consequences of that.
Second, he ascribes the view that humanity is the source of all value, not to Christian theologians, but to "Pagan philosophers". Thus, the Renaissance has sometimes been seen by low and scurrilous sorts of people as merely a rebirth of ancient Grecco-Roman humanism.
The reason he could do this is because Christian scholars ─ pretty much the only scholars, back then ─ had been rediscovering Classical thought, particularly via Spain and the Moors.
... Renaissance humanism, although heavily inspired and informed by humanistic Grecco-Roman philosophies, etc, also owed a lot to Christianity. Bushels and bushels, in fact!
Bear in mind that Christianity was heavily influenced by Greek thought to start with. It's written in Greek, it gets its ideas about the soul and post-mortal judgment and heaven and hell from Plato, the eucharist is based on a Greek practice (consuming bread and wine in conscious honor of Demeter and Dionysos), taking your staff, walking the roads, encountering people and talking to them, and trusting in providence for your food and drink is pure Cynic teaching, and so on. As a result of the Renaissance, Christian thought became even more heavily neo-Platonist, and their cosmology even more Aristotelian until (Copernicus and) Galileo.
The notion that everyone is equal on the level of the soul (and somewhat later on the notions that everyone ought to be equal before the law, have equal opportunities in life, etc, etc.) would have been inconceivable to classical thinkers such as Plato and Aristotle. Those thinkers accepted as fact that some lives -- usually the lives of the poor and powerless -- were of less worth and value than other lives -- usually the lives of the rich and powerful.
No doubt about that. Everyone who mattered back then equated equality with anarchy. Paul in effect says as much.
But there's likewise no doubt that Athenian democracy was seized on by humanists and waved as a flag once things got political. (Not so much the Roman republic, whose fall brought in the Golden Age of Empire and the Caesars and founded modern Europe.)
Christians, on the other hand, saw everyone as equal before God.
Er, throughout the Renaissance Europe was ruled by monarchies, all of whose monarchs, with the enthusiastic backing of the Church, declared themselves God's Anointed Ruler. The Vatican is still an autocracy with clearly defined lines of hierarchical authority. And the Brits were singing 'The rich man in his castle, / The poor man at his gate, / He made them high or lowly, / He ordered their estate', a verse from 'All Things Bright and Beautiful' that was quietly dropped but not till the 1950s or so. The British, French, Yankees and more were enthusiastic slave-owners and traders, including Jefferson while penning 'All men are created equal', and they all found more than ample support from both the Torah and Paul.
So equality in the West is a confused picture, in which Classical learning, its offspring humanism, strands of Christian teaching, and the rise of nonconformism within Christianity, played a part.
Oh, and as for the equality of women, all but nothing happens till the 20th century, and Christianity has hardly been their friend along the way. Kinder, Küche, Kirche, as the Germans say, or used to.