To give an example within the realm of intellectual history, teleological intellectual histories very often create the false impression that the only figures involved in a period’s intellectual world were heroes and villains, i.e. thinkers we venerate today, or their nasty bad backwards-looking enemies. This makes it seem as if the time period in question was already just previewing the big debates we have today. Such histories don’t know what to do with thinkers whose ideas were orthogonal to such debates, and if one characterizes the Renaissance as “Faith!” vs. “Reason!” and Marsilio Ficino comes along and says “Let’s use Platonic Reason to heal the soul!” a Whig history doesn’t know what to do with that, and reads it as a “dead end” or “detour.” Only heroes or villains fit the narrative, so Ficino must either become one or the other, or be left out. Teleological intellectual histories also tend to give the false impression that the figures we think are important now were always considered important, and if you bring up the fact that Aristotle was hardly read at all in antiquity and only revived in the Middle Ages, or that the most widely owned author in the Enlightenment was the now-obscure fideist encyclopedist Pierre Bayle, the narrative has to scramble to adopt.
Teleological history is also prone to “presentism” <= a bad thing, but a very useful term! Presentism is when one’s reading of history is distorted by one’s modern perspective, often through projecting modern values onto past events, and especially past people. An essay about the Magna Carta which projects Enlightenment values onto its Medieval authors would be presentist. So are histories of the Renaissance which want to portray it as a battle between Reason and religion, or say that only Florence and/or Venice had the real Renaissance because they were republics, and only the democratic spirit of republics could foster fruitful, modern, forward-thinking people. Presentism is also rearing its head when, in the opening episodes of the new Medici: Masters of Florence TV series, Cosimo de Medici talks about bankers as the masterminds of society, and describes himself as a job-creator, not the conceptual space banking was in in 1420. Presentism is sometimes conscious, but often unconscious, so mindful historians will pause whenever we see something that feels revolutionary, or progressive, or proto-modern, or too comfortable, to check for other readings, and make triple sure we have real evidence. Sometimes things in the past really were more modern than what surrounded them. I spent many dissertation years assembling vast grids of data which eventually painstakingly proved that Machaivelli’s interest in radical Epicurean materialism was exceptional for his day, and more similar to the interests of peers seventy years in his future than his own generation — that Machiavelli was exceptional and forward-thinking may be the least surprising conclusion a Renaissance historian can come to, but we have to prove such things very, very meticulously, to avoid spawning yet another distorted biography which says that Galileo was fundamentally an oppressed Bill Nye. Hint: Galileo was not Bill Nye; he was Galileo.