Larry Norman's The Shock of the Ancients goes into this a great deal. It was essentially in the immediate cultural aftermath of the Italian Renaissance that the ancients stopped being seen as an eternal model of emulation and began to be seen as simply a precursor to the even greater modern age. This perspective eventually set off what was called "the Quarrel of the Ancients and Moderns" in which the various courtiers in Louis XIV's wrote competing works on whether the modern age surpassed the ancient one. Interestingly, the quarrel itself was purely over literature, art and, to a lesser extent, philosophy, and it was initiated by panegyric to Louis by one Charles Perrault that essentially said that, in much the same way that the moderns surpassed the ancients in science and technology, so to in art, wisdom in justice.

As a note, the general assessment you hear is that it was between the conservative Ancients and forward thinking Moderns, and that it resulted in complete victory by the latter, but this isn't precisely true. Norman's argument is essentially that the Ancients were actually conducted some fairly sophisticated social critiques, and that the Modern position was more about glorifying Louis than staking a progressive position. And even beyond that, Racine, perhaps the most enduring literary figure of the period, was an avowed Ancient and rather later Rousseau, although too complex to be put in either box, generally picked up the thread of the Ancient arguments.

Not exactly what you are asking, but it was during dissections in the Renaissance that artists first noticed discrepancies between their observations and ancient authorities like Galen. The original aim of the humanists was to revive classical Latin and classical literature, not to replace it.