'We' were the first modern republic if my knowledge is correct. How and why did the Dutch became a monarch? In my mind monarchies are established through force and repression. I have no knowledge of the Dutch royal house using force to come to power, which leaves me to conclude that the Dutch accepted the transition to place power in a monarch.
How did this transition occur and if my conclusion that this process was peaceful is correct, why was this accepted when so many other countries fought to get rid of their monarchs?
The success of the House of Orange to be rulers of the Netherlands is due to (1) judiciously escaping for his life when other strong leaders didn't (and paid for it with their lives), (2) ability and willingness to compromise during periods of weakness, (3) great luck as external factors distracted their arch nemesis the Spanish at opportune times, and (4) wise investment just in time for resumption of hostilities.
Religion and the failure to compromise
The Dutch rebellion initially started due to religion, as Protestantism (in particular Calvinism) took hold in areas of the Low Countries then-ruled by Philip II of Spain as part of his Burgundian inheritance. Since the beginning of his rule, Philip had attempted to maintain religious orthodoxy by reducing the powers of local bishops and priests, and to introduce the Spanish inquisition. Things came to a head in the 1560s as open-air sermons added a strong flavor of populist violence, as churches, monasteries, chapels were swept up in the Beeldenstorm or iconoclasm. The then-regent, Margaret of Parma, tasked William Orange, Lamoral Count of Egmont, and Philip de Montmorency, Count of Horn, to negotiate peace with the belligerents. The populist tone of the Beeldenstorm made both Catholic and Protestant nobles worry.
These three local leaders had suggested compromise, and the last two (not William Orange) even traveled to Spain to ask Philip II in person to give some tolerance to the Protestants. The two were military heroes and had recently led Philip's army victoriously against France.
When they returned to the Low Countries, they had interpreted Philip's reaction as agreeing with their proposal. However, due to the outbreak of the Beeldenstorm and further violence, Margaret the regent wrote an alarming letter to Philip II claiming that rebellion was at hand.
As a result, Philip changed his mind and opted for a military solution, sending the Duke of Alba who was considered the most able military commander at the head of the so-called Army of Flanders. They marched up to Brussels successfully and set about pacifying the Low Countries.
Egemont and Montmorency, not unreasonably, expected to be able to still negotiate a peaceful settlement with the Duke of Alba. They considered themselves loyal subjects of Philip II and further they had previously expected Philip himself to travel to the Low Countries and thus nothing severe would be decided until then. William Orange, on the other hand, fled to Palatine and Saxony. In the end, the first two were wrong. The Duke of Alba decided on the strongest possible punishment, namely death sentences to those two. Philip's own personal preference is still under debate, although most historians believe that his vague instructions to Alba was interpreted in the most severe way. Philip himself was in mourning after the loss of his third wife Elisabeth of Valois, whom he loved very deeply.
So instead of three possible leaders of the "Dutch revolt", there is only one clear one left, namely William Orange.
I have written a bit on the topic, in particular about the compromises that William Orange had to make in order to maintain a semblance of unity among the rebels.
An unruly motley of rebels
The northern states couldn't agree on religion. When they declared the Union of Utrecht in response, northern states contained a mix of militant Calvinists and more moderate Catholics. Finally, if they were going to reject Philip II's rule, they couldn't agree what would be the new government. Holland was a rising state, following Antwerp's misfortune, and other northern states did not want their political influence to be reduced and be Holland's weak powerless siblings. This set the stage for the Act of Abjuration of 1581, which declared the United Netherlands to be independent from Philip II of Spain, followed the declaration of the Union of Utrecht by the northern states. Thus, the Union of Utrecht was reactionary and purposefully did not specify a strong central government, the reason being Orange was convinced (1) his position relative to the states was weak, (2) they had to compromise between radical Calvinism and Catholicism in the north, and further (3) the Spanish were making advances everywhere.
Appeal to foreign help
As a result of this compromise and lack of central government, Orange had invited Francis, French Duke of Anjou, to become a titular head of state of the United Netherlands. The goal was two fold, the United Netherlands felt they needed France's military support, second to encourage more loyalty from the constituent states by appealing to former glory of the Burgundian Netherlands, in the older period under a French royal house. As such, Anjou was intended to be a figurehead and his powers were very limited.
Continuing losses to the Spanish Army of Flanders led to frustrations on all sides, culminating in Anjou's attempt to outright take control of several key cities in Brabant and Flanders. This failed, and an embarrassed Anjou retreated to Holland effectively powerless and remained there for the rest of his life. Orange then again became the effective head of state, but with significantly reduced prestige. Importantly, Holland's relative power had increased, as Brabant and Flanders came fully under Spain's control, and Orange had to accept stronger Calvinist policy against Catholicism. Towards the end of his life, he himself converted to become a Calvinist.
Things did not immediately become rosy, as further in 1585 they had to accept the Treaty of Nonsuch to become a protectorate of Elizabeth of England, who was compelled to directly support the Netherlands following the massacre of Protestants in France, eventually leading to the outbreak of the French Wars of Religion. Brielle and Flushing were given to England, and was garrisoned by English troops. There were also trading compromises.
Serendipitous religious wars elsewhere, an important breathing space, and internal religious compromise
While the presence of English troops led by Earl of Leicester helped, things were still dire until 1588. William Orange was assassinated in 1584, and his son Philip William had been seized to be raised in Spain as a good Catholic and loyal subject. Fortunately for the Dutch rebels, the Spanish succeeded in the former but not the latter; when Philip William returned to the Low Countries he proved to be loyal to the Dutch rebels although as a loyal Catholic he restored Catholic service where he could. On the other hand, he allowed the staunchly Calvinist faction to increase their political influence in the major cities. This strengthened the compromise that his father had started. When he died, his younger brother Maurise of Nassau who was a Calvinist proved to be an able military and political commander, just in time.
Once again, the presence of foreign troops -- this time English -- once again led to arguments between the states. What truly helped the Dutch were the need to build a Spanish armada to invade England, and the need to direct Spanish resources into the French Wars of Religion. The breathing space afforded allowed the Republic to build its troops, build fortresses in the new trace italienne style, which significantly strengthened their defense and increased the cost of sieges, and further engage in state building. All these investments helped them stop Spanish momentum in re-capturing the rest of the Netherlands, despite lack of cohesion as Philip William and later Maurice of Nassau needed time to build both political cohesion and military strength.
The military successes of Maurice of Nassau/Orange in Turnhout (1597) and Nieuwpoort (1600), using his new "Mauritian army model" afforded him significant political power and prestige, which allowed him to further unite the various states just in time for the 12-year Truce negotiated with a bankrupt and over-stretched Spain. The 12-year Truce saw further fortifications built, meaning that the border between the Dutch rebels and the Spanish Netherlands became more strongly defined.
The end of the Truce could have been another difficult time for the Dutch, however the outbreak of the Thirty Years War in Germany meant Spanish and Habsburg attention was diverted, and importantly France started to take an active interest in supporting the Dutch.
Sources:
G. Parker, "Why Did the Dutch Revolt Last Eighty Years?," Trans. Royal Historical Society, vol. 26, December 1976.
G. Parker, "Imprudent King: A New Life of Philip II," ISBN-13: 978-0300196535, 2014.
J. Israel, "The Dutch Republic: Its Rise, Greatness, and Fall, 1477-1806."