Croatian here. This is quite a long story but for the sake of narrative i will leave many things out of it.

Before the World War I there was strong enthusiasm for pan Yugoslavianism among Croatian, Slovenian and some Serbian intellectual elites. Basically they saw in in unity among South Slavs a solution to defend from what they saw as German and less from Italian encroachment. Many of them sincerely believed that new state would be a free democratic union of brotherhood nations.

During the WWI Austro-Hungary suffered from war exhaustion and Vienna was unable to find solution for significant discontent now arising among different ethnic group. There was a group of South Slavic politicians in AU who wanted to make deal with Vienna within framework of AU institutions (more democratic freedoms, less centralization), but crumbling and ineffective response from Vienna turned even them against staying in said union. What was worse London treaty, some trappings of it came to light to Slovenian and Croatian politicans. This caused panic and turned great majority of them toward hurried union with Serbia. Serbia as one of members of Entante which had good relationship with France and Russia, was only solution to save many of their compatriots from Italian yoke. So during last months of 1918 South Slavic lands of AU declared independence formed provisionary ad-hoc goverment to negotiate Union with Serbia. But Italian troops were quick to seize Croatian coast and parts of Slovenia and Serbian troops poured from the east. Facing with shrinking territory and with no means to defend itself, new goverment despite some opposition declared itself under the rule of Belgrade to save what they could.

28.06. 1921 a new constitution was promulgated. During voting two different ideas came forth how state should be governed. Majority of Serbian politicians saw new state as merely expansion of Serbia, and along with some allies in new lands had promulgated a unitary constitution which abolished all regional parliaments and formed highly centralized state. Among Croatian and Slovenian politicians who advocated for federated state this caused major distress because centuries of political traditions were swept away overnight.

New state proved itself unstable. In Belgrade King supported by powerfull army was constantly meddling in government business. He viewed with suspicion most powerfull Serbian party; People's Radical Party due to its liberal and revolutionary past and was often at odds with its immortal leader Nikola Pašić. Also goverment was not able to effectively rule in new areas due to the passive opposition of common folk. Also problematic was constant promotion of Serbian interests, indeed majority of political, military and economic ruling class was composed mostly by Serbians, and members of other ethnical groups were often excluded from powersharing.

In Croatia new opposition leader had emerged. Stjepan Radić as leader of Croatian Peasant Party became de facto leader of Croatia always winning vast majority of votes in Croatia. Advocating for federalization and new constitution he became thorn in the side of Belgrade.

Political deadlock had emerged, with many reforms unable to be promulgated due to the weakness of parliament and goverment. During one particulary heated discussion in the parliament member of People's Radical Party shoot shot Stjepan Radić and several other members of Croatian Peasant Party, Stjepan Radić would die several months later due to wounds caused by the bullet. This caused significant unrest in Croatia. It was highly suspected but not proven that hit was ordered by King himself, because assassin Puniša Račić was member of King's circle of confidants and also because the Račić was punished by "prison" in luxurious villa in center of Belgrade.

Faced with crysis, at beginning of 1929 King abolished parliament and goverment and declared what he saw as temporary dictatorship. Intially move was greeted by many because they saw the King as only force capable of restoring Yugoslavia. But soon intial benevolence turned to heavy handedness. All political parties were abolished, and many members of opposition soon faced political persecution which saw many of them either exiled or put into the prisons. There was widespread censorship and prohibition of free speech and members of police and military had free reign in carrying out nationwide murders and beatings of political opponents. Instead of fresh start under the mantra of fair Yugoslavia, state became oppressive and undemocratic where key positions were staffed by King's lackeys. Also widespread Great Depression came knocking on the door.

Harsh policies angered many Croatian nationalists and there emerged a movement called Ustaše. They called for violent overthrow of current regime seeing this as only way for establishment of free Croatia. They advocated any means even murder to establish free Croatia. They did not manage to gather mass following but during the chaos of WW2 they came to power. In 1934 Ustaše allied themselves with Buglarian seperatists in Macedonia, and carried out assassination of King Alexander I during his visit to France in Marseille. Instead of crumbling, Yugoslavia endured, and due to the youth of the new King, his cousin Prince Pavle took control. Many of the draconian laws were abolished, some democratic freedoms were established, but heavy hand of state was still felt, it was something of "Guided democracy", also idea of federalization was not seriously discussed. new regime proved more stable than the old ones. Prime minister Milan Stojadinović proved as competent politican eliminating some effects of Great Depression. But at begining of 1939. Stojadinović clashed with Regent. He had advocated allying with Italy and Germany and had started to imitate Duce. He was dismissed and new goverment was formed with explicit order by regent to make some kind of a deal with Croatians. Regent was worried by rise of Italy and Germany and believed if he could make deal with Croatians the state would be much stable. Cvetković-Maček agreement angered many but left nobody satisfied, Serbian elements thought Croatians got too much, Croatian elements were not happy with "rump state", and other ethnic groups were unhappy because they did not get similiar autonomy. With other neighbours quickly joining up Axis, regent saw new chance a signed highly controversial agreement which put Belgrade into the German sphere. A coup was launched and regent was removed from power, and war came knocking on the door.

Tl;dr New state was highly controversial. Much of the power was concentrated in the hands of Belgrade, completetly disregarding desire for autonomy of many ethnic groups especially Croatians who as second biggest group were unhappy because their political traditions were swept away overnight. This caused some Croatian elements to form radical group with explicit violent tendencies who saw all Serbs as violent opressors of Croatian desire for independence, their ideas were formed as reaction to opression endured during dictatorship of King Alexander I.

Most of my sources are in my native tongue but some English one.

Glenny, Misha. The Balkans: Nationalism, War and the Great Powers, 1804-1999 (Penguin Books, 1999)

Dejan Đokić, Elusive Compromise: A History of Interwar Yugoslavia" (2007)

Dejan Đokić, Yugoslavism: Histories of a Failed Idea, 1918-1992 (2003)

Sadkovich,James j. Italian Support for Croatian Separatism (1987)

Jelavih, Barbara, History of the Balkans: 20th Century (1983)

Edit: Excuse my poor grasp of English