It's a little bit of medieval politics centered around St. Thomas Aquinas.
St. Thomas had a strong connection to the Dominicans, having received the habit of St. Dominic twice (it's a long, unrelated story) and defending them in a dispute between the friars and the University at which he received his Doctorate of Theology. His works became part of the core teachings of the Dominican order, especially after his death.
Now, St. Thomas was commonly believed to have opposed the idea of the Immaculate Conception, stating in the Summa:
The sanctification of the Blessed Virgin cannot be understood as having taken place before animation, for two reasons. First, because the sanctification of which we are speaking, is nothing but the cleansing from original sin: for sanctification is a "perfect cleansing," as Dionysius says (Div. Nom. xii). Now sin cannot be taken away except by grace, the subject of which is the rational creature alone. Therefore before the infusion of the rational soul, the Blessed Virgin was not sanctified.
Fast-forward a few years later to when Bl. Duns Scotus starts to formulate the doctrine of the Immaculate Conception as we know it today. He provided the biggest defense of the Immaculate Conception to date; or as the Catholic Encyclopedia puts it:
He showed that the sanctification after animation — sanctificatio post animationem — demanded that it should follow in the order of nature (naturae) not of time (temporis); he removed the great difficulty of St. Thomas showing that, so far from being excluded from redemption, the Blessed Virgin obtained of her Divine Son the greatest of redemptions through the mystery of her preservation from all sin.
Gradually, all the universities and orders began to adopt Scotus's position. The Dominicans, on the other hand, were obliged to follow their brother Thomas (who formed much of their order's early theology), rejecting Scotus's "workaround." It took a few hundred more years of interpreting St. Thomas's works until they eventually came around.
In hindsight, it appears that people were working off of different terms, or as the Catholic Encyclopedia puts it:
In the thirteenth century the opposition was largely due to a want of clear insight into the subject in dispute. The word "conception" was used in different senses, which had not been separated by careful definition. If St. Thomas, St. Bonaventure, and other theologians had known the doctrine in the sense of the definition of 1854, they would have been its strongest defenders instead of being its opponents.