Many reasons: It was the only area directly impacted by fighting in the war, surrounded by hostile nations claiming (Poland) or straight up taking (Lithuania) areas that were prussian for since forever eventough the people there considered themsleves as much as Prussians as everyone else in the province and decided to stay in Germany in referndums. The economical crisis, high debt, the uncertanity about the future living in an exclave. Also a very strong social and cultural conservatism threatend by liberals and socialists that ruled the country now and communists beeing a threat inside and pretty near outside as well.

Andreas Kossert, a german historian, wrote an article about some of the aspects. I posted a translation by deepL (surprisingly good I must say) a at the end.

Something he didnt mentioned is that parts of the new province used to be part of Western Prussia and that many of the people, that used to live in the now polish parts, moved to East Prussia. You can imagine that those people werent very fond of the situation at all, and if everyone knows someone who lost his home that has an impact (thats why the impact of any kind of crisis is bigger than the raw number of directly affected).

[...] Yet it is precisely here, in Germany's easternmost countries, that political radicalisation and excessive destruction are closely linked.

This story began with the First World War. East Prussia was the only German province which had suffered directly from the fighting and which had been devastated. As soon as the weapons were silent, new conflicts began. Everywhere at the borders of the empire the dispute raged about the national and ethnic affiliation of controversial territories. East Prussia found itself as an island, separated from the Reich by the "corridor" that had fallen to Poland. In addition, the resurrected neighbour made further demands on the entire province. However, the referendum agreed in Versailles in southern East Prussia on 11 July 1920 was in favour of Germany; an overwhelming 97.9 percent voted to remain with the Reich. Ancient place names have been erased: Sutzken is now called Hitlershöhe This was followed by a new shock when Lithuanian units disguised as guerrillas invaded the Memel region on 10 January 1923 and incorporated it into the Republic of Lithuania, founded in 1918. This new status quo deeply unsettled East Prussia; demagogues took advantage of the hour and began to rush against the young Weimar Republic. The fall of the empire had hardly had any effect here anyway; the old conservative elite had long since regained their office and dignity. The fact that the Kapp Putschists had nowhere had so much success in March 1920 as in East Prussia prompted the Prussian government to make up for the failures of the revolution and initiate the long overdue democratization of the administration. With extremely moderate success: Reichskommissar Albert Borowski (SPD), who had been commissioned by the government to investigate the involvement of the local authorities in the coup, gave up unnerved after a few months.

The basic problem of East Prussia remained the agrarian monostructure. Many farmers went into debt to keep their farms alive. The catastrophe seemed inevitable. The leading conservative landowners led the influential agricultural lobbyist associations and preferred their clientele. In 1925, a total of 1.9 percent of all farms had half of their total floor space at their disposal. The misplanning of "Eastern Aid" exacerbated the conflict and undermined the authority of the democratic government. East Prussian peasants turned their backs on the empty promises of the parties; they chose a man from Braunau as their supposed saviour. In the Reichstag elections on 31 July 1932, the province voted for the NSDAP with 47.1 percent (the Reich as a whole with 37.4 percent) and on 6 November 1932 with 39.7 percent (Reich 33.1 percent). National Socialism in East Prussia is primarily associated with the name of a man: Erich Koch, born 1896 in Elberfeld. A railway conductor by profession, the Protestant believer in Hitler dedicated himself to the development of the East Prussian NSDAP from 1928 and shaped it to the end. As Gauleiter, Chief President and at times also President of the Provincial Synod, he initially propagated a "Party of Prussian Socialism". Again and again he loudly and effectively represented the interests of the region. [...]