I'm a medievalist by training, although I started out as a classicist, moving gradually into "late antiquity" before eventually focusing on the 13th century for my doctoral work.
The term "medieval" (from the Latin medium aevum) was originally coined by the Italian Humanists to denote the time in between the classical world (particularly Rome) and their own age, which saw a revival of interest in classical Latin arts and culture. The Humanists very strongly believed in focusing directly on classical-era literary sources rather than on what they saw as the old-fashioned scholarship that had been the focus since. We often call this period "the Renaissance", but in humanist parlance, what was being "reborn" was direct knowledge of the classics as well as of religious texts, turning away from the dominant method of scholarship (known as scholasticism) that had dominated the medieval European universities since the 12th century.
What happened in the ensuing centuries, especially during the Enlightenment era, is that "medieval" began to be viewed as a period of decline and superstition between the fall of Rome and the Renaissance, where all of the achievements of the classical world were somehow lost before being rediscovered by the humanists. In the English-speaking world, Edward Gibbons' History of the Decline and Fall of the Roman Empire became seminal in promoting the idea that Rome declined because of a loss of civic virtue, its decadence weakening it until it was toppled by the barbarians. The ensuing Middle Ages, in his view, was an age of superstition (and Gibbons being English, this was specifically Catholic superstition) that retarded its advancement into enlightenment. "Medieval" definitely had a pejorative meaning for Gibbons.

This became the dominant popular narrative of the Middle Ages all the way into the 20th century. In the United States, for instance, this narrative features prominently in the Story of Civilization of Will and Arial Durant, a highly-influential, multi-volume popular history in the United States, and has not ever completely subsided (for example, William Manchester's very popular A World Lit Only By Fire relied heavily on it.) More recent scholarship has focused more on the continuity of society through the end of the Roman world and continued technical, cultural, and artistic development in the medieval era, as well as at least two "renaissances" of learning that took place in the 8th century (in the Carolingian era) and the 12th century (with the rise of universities, including the influence of Islamic scholars such as Averoes and Avicenna).
To a medievalist, "medieval" isn't really a slur, but medievalists also vigorously fight the idea that the world dwelt in darkness and superstition after the "fall of Rome" until suddenly, poof! It was the Renaissance and civilization was rediscovered.

For further reading: This is such a broad era, but Rosamund McKitterick's The Carolingian Renaissance is a seminal work in understanding this crucial period in European history, where most of the surviving copies of classical works were actually made (so much so that the Italian humanists, believing that these copies were the works of the Romans, adapted the Caroline miniscule script found in them as Humanist minuscule in imitation of what they believe to be "Roman" script.)