What today is Sweden, Finland, Denmark, Norway, and Iceland were during the 15th century united, at least de jure, in the Kalmar Union. However, that union broke apart during the early 16th century, so at the same time as the Lutheran reformation started. Hence, you need one answer for Denmark, Norway, and Iceland and a separate answer for Sweden and Finland. My answer is with regards to Sweden and Finland. Or rather with regards to Sweden, as Finland turned Lutheran simply because Sweden turned Lutheran as they were one country until 1809 that was ruled from Sweden.

First, the reason Sweden turned Catholic to begin is because the christianization of Sweden was mainly done by the Germans. The christianization began in the 9th century by bishop Ansgar from Bremen, according to Vita Ansgarii by Ansgars successor Rimbert, and the process was subsequently handled by others from Germany and England. Simply put, Sweden became Catholic as it was Catholics that turned Sweden Christian; which is not all that odd given proximity.
(I find no good summary in English, but here is a Swedish source popularhistoria.se/sveriges-historia/nar-sverige-blev-kristet)

Second, the reason why Sweden did not stay Catholic has to do with the dissolution of the aforementioned Kalmar Union. Already back in 1434 did a man named Engelbrekt gather followers for a revolt against the king of the Union. This revolt was the start of roughly hundred years of civil war, that in part was regarding Sweden's independence from the union; with one side always being on the side of the union king and the other side opposed. The beginning of the end of the civil war came in November 1520 with what is called the Stockholm Bloodbath, in which the then Archbishop of Sweden Gustav Eriksson "Trolle" first excommunicated the parliament (with approval from the then pope Leo X) and then had all he could get his hands on executed. However, one man that he failed to execute was a young noble named Gustav Eriksson "Vasa", even though Trolle did manage to kill Vasa's father, who managed to flee north where we raised an army that in 1521 helped him retake Stockholm and send Trolle into exile. Vasa did get a demand from the pope to let Trolle return as archbishop, but refused and as such remained excommunicated. Hence, when he in 1523 made himself king, despite lacking any real claim to the throne, was a return to Catholicism not an option.

(Once again unfortunately no good sources in English. But the books "Uppror och allianser" and "Stockholms blodbad" by Dick Harrison and "Svea rikes ärkebiskopar" by Åsbrink and Westman are good books on this period of Swedish history)

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Third, by 1523 did Sweden then stand with hundred years of civil war behind it, a bloodbath that had exterminated a lot of the nobility, and a king who was both poor, illegitimate, and excommunicated. Hence, Catholicism was as previously mentioned not an option for this new king, given the excommunication. Going at it alone like Henry VIII did in England would have been an option, but not a good one given that he already was poor and illegitimate. And turning to the Orthodox who were both far away and rather recently had suffered the fall of Constantinople is nothing I've ever heard him even considering. Therefore, joining with the Lutherans of northern Germany was the option that he went with. Worth noting though is that even though the move toward Lutheranism began already 1523 so did it become final first in 1544.

In short answer, the cultural and educational connection between (northern) Germany and Scandinavia in the end of the Middle Ages played an main role, then the secondary factor was the political development and competitions within Nordic kingdoms that occurred after the separation of Sweden from ex-Kalmar Union in the 1520s.

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• How did Scandinavian countries become Protestant while much of Europe remained Catholic answered by /u/Platypuskeeper summarized the basic timeline and important events in the Reformation in Nordic kingdoms in the 1520s and 1530s.
• My answer in Is there any reason why most of Romantic and (western) Slavic Europe stayed Catholic, whereas most of Germanic Europe went Protestant? focuses more on Scandinavian students and almnis of German universities.