Part of the reason you are having difficulty coming up with a clear argument is that Czechoslovakia was not split by the Germans, so what happened in Slovakia was not entirely the Germans’ decision. The historical context is important as well, and I think that might be a good place to start.

Since it was founded in 1918, Tomáš Masaryk’s government had proclaimed the First Czechoslovak Republic to be a bulwark of Western liberalism and democracy with a historic mission based on Czech national identity. However, as a highly industrialized country deeply impacted by the Great Depression, Czechoslovakia was already on shaky ground in the late 1930s. When Masaryk died in 1937, his successor Edvard Beneš was unable to do much with the fraught domestic politics he inherited. Konrad Henlein’s Sudeten German Party was just one of the groups who were challenging the Czechoslovak state at this time. Communists, clerical conservatives, rural fascists, and other groups dissatisfied with the status-quo were beginning to seriously challenge Masaryk’s democratic, Western-oriented vision for Czechoslovakia. So when the Munich Agreement happened in September 1938, that vision was severely delegitimized at a time when it was already under siege.

In October and November, the First Czechoslovak Republic collapsed. Slovakia and Carpathia Ruthenia both formed autonomous governments, Beneš resigned and left for England, and the Czecho-Slovak Second Republic was declared in November. The Second Republic had a strict two party system led by a combination of clerico-fascists and anti-democrats whose entire foreign policy centered on preventing further German expansion at their expense. In January 1939, Czecho-Slovakia withdrew from the League of Nations, signed the anti-Comintern Pact, and began instituting anti-Jewish policies modeled on the Nuremberg Laws. The problem with that plan was that some of the most important industries in the country still desired by Germany were not in the Sudetenland, including most of the armaments industries like Škoda and Zbrojovka Brno. Before Munich, Czechoslovakia was the 10th most industrialized country in the world, and had the 7th largest armaments industry. Racial politics and Lebensraum were incredibly important forces behind the annexation, but the economic motives should be kept in mind. With some notable exceptions, the subsequent German occupation of the industrialized Protektorat Böhmen und Mähren and its large armaments industry was focused on economic exploitation and converting Czechs into Germans.

The reason I have brought this all up to answer your question is that the German invasion in March 1939 was in response to Slovakia declaring independence on the 14th. This was somewhat at the behest of the Germans, but Jozef Tiso’s autonomous Slovak government had already moved away from the idea of a multinational Czechoslovak state by the time the final invasion took place. When President Emil Hácha surrendered the country and the Germans moved in on the 15th, it was done under the pretense of looking after a failing state and helping Slovakia to gain independence.

As to your ethnic question, it is important to remember that the Czech portion of Czechoslovakia (Bohemia, Moravia, Czech Silesia) was not homogeneously Czech at that time. Nationality is a social construct anyway, but nationalities were especially fluid categories in parts of Central Europe at this time. As Chad Bryant puts it, nationality was “something acted out in civil and political society” at the individual level instead of something imposed on you by the state. Once the Germans took over, it was still possible to jump across the lines as it fit for a time, but eventually that began to harden when the requirements to become a registered Protectorate German were raised. By 1940, the economy had been fully integrated into the German war effort and 'acting nationally' was restricted.

Among the Nazi racial planners, there was a real sense that Czechs were some form of wayward Germans who could be brought back into the fold by re-Germanizing them. Based on "research" done in 1940 by the German race-scientist Karl Müller, Nazi officials accepted the argument that Czechs had a mix of Slavic and German blood, but the German blood was still quite strong and could be cultivated in a way that could undo the effects of the last century of Czech nationalism. To do this, the Protectorate government began to try and separate those with more German blood from those with less, which would keep the industrial and agricultural productivity going in the region without needing to transfer large new populations in. Of course all of this is absurd, but that's early 20th century race science for you. As an aside, it was partially this plan to re-Germanize Czechs that caused Konstantin Neurath to be replaced by Reinhard Heydrich as Reichsprotektor in 1941 because Neutrath was accused of not being selective enough in this re-Germanization process.

To summarize, there were several reasons that the Germans annexed the Czechs and left the Slovaks. They wanted to directly control Bohemian and Moravian industry, the Czechs were seen as potential Germans, and Slovak secession was the catalyst for the invasion in 1939.

Sources:

Tomáš Masaryk, The Czech Question , 1895.

Chad Bryant, Prague in Black , 2007.

Bradley Abrams, The Struggle for the Soul of a Nation: Czech Culture and the Rise of Communism , 2004.

Jaroslav Pánek et al, A History of the Czech Lands , 2009.

EDIt: corrected 1942 to 1941 in the sentence about Heydrich’s appointment as Reichsprotektor