This is something I have often wondered about. All Christians believe that Jesus is the Son of God, right? So, why all the various Churches?
And why is Christianity right and not Islam or Judaism or Buddhism etc.?
Human beings have a fairly strong proclivity toward disagreeing and having differing opinions.
At any rate, denominationalism is a sort of strange feature of Protestantism. As a rule Roman Catholicism and Eastern Orthodoxy aren't considered "denominations" as such, but rather "denominations" tends to describe the organizational structures within Protestantism.
I say "organizational structures" because even churches of the same theological tradition (e.g. Lutheranism) are split into various ecclesiastical bodies. My denomination is the ELCA (Evangelical Lutheran Church in America), the second largest number of American Lutherans belong to the LCMS (Lutheran Church--Missouri Synod). Both the ELCA and LCMS are Lutheran; but we're different denominations of Lutheranism.
There is no single reason why this is. It's usually more helpful to investigate the history of each denomination and tradition to see how it developed within the broad spectrum of Christian history and tradition.
Going back to Lutheranism, Lutheranism came out of the 16th century Protestant Reformation. It would be easy to say, "Martin Luther broke away from the Catholic Church and started a new one" but that's not true. Luther didn't break away from the Catholic Church; Luther identified himself as a faithful Catholic, as did all the early Lutheran reformers. And then there's the term "Lutheran", it's misleading. Luther remarked once that it was terrible that "[Christians] should call themselves by my wretched name". "Lutheran" was an exonym. The term Luther and the other reformers used was "Evangelical" (German: "Evangelische", which is still the German word for "Protestant").
For Luther the goal was a reform of the Catholic Church from within, to reinvigorate the Church with the purity of the Christian Gospel (Greek: "Euangelion", the "Evangel" of "Evangelische").
However the result was that the Pope gave a bull of excommunication, and thus Luther was regarded by the powers that be in Rome as outside of the Church catholic; whereas Luther regarded the papacy itself to be outside of the Church catholic and such the papal bull worthless.
That meant schism, a severing. Luther and the evangelical reformers on the one side, and the Pope and papal supporters on the other. Both regarding themselves faithful Catholic Christians, and being faithful to the ancient catholic faith of the Apostles, Church Fathers, and Ecumenical Councils of the undivided (pre-1054 AD) Catholic Church.
But that's just one tradition within the umbrella group of "Protestantism". To understand then how there are now, for example in the United States, multiple Lutheran denominations it becomes more complicated. Lutheranism came to North America through waves of German and Scandinavian immigrants; mostly in the 1800s. These early Lutheran immigrant communities retained the culture of the homeland, their services were in their traditional tongue, and so forth. Homegrown Lutheran congregations developed, and eventually English dominated with succeeding generations.
The late 19th and early 20th century saw a rise of Liberalism in Europe, and it also made it to American shores, and it split Protestants of all sorts apart on various issues of theology and biblical practice. The 20th century saw an increase in social issues which created rifts along political and social lines in church bodies, and Lutheranism was no exception.
So these are all the sorts of circumstances that have--and continue--to develop the American Lutheran identity. Church-wide bodies split over social issues, and smaller church bodies rejoined with others to produce larger ones (the ELCA came about through a merger of several Lutheran bodies in the US).
And then there's the issue of ecumenical work, pan-ecclesiastical cooperation and work, etc. For example, the ELCA is a Lutheran denomination within the United States, but works in cooperation with Lutheran bodies from all over the world through, for example, the Lutheran World Federation. And thus functions within a larger Lutheran framework. The ELCA is also part of a global ecumenical body known as the World Council of Churches. Domestically, the ELCA also has what is known as "altar and pulpit fellowship" with several other mainline Protestant bodies, the Episcopal Church, the United Methodist Church, and the Presbyterian Church USA (maybe more, but those are the ones I remember off the top of my head).
And that's just Lutheranism and the ELCA.
Understanding the situation means there is no one size fits all. Instead one needs to understand the history and circumstances of each case.
-CryptoLutheran