WHAT Did the Germans Have Against the Slavs, in WWII?

Like with others, it was because of their perceived "racial inferiority".

(That's if you mean by "Slavs" Slavic peoples [Poles, Russians, and others]).

How does one explain racism and the fallacies behind it?

Why not see all those infinite master race claptrap?

Reasoning...what reasoning?

There's no logic to that racist propaganda. It was a tool.

It's clear that Hitler worked on eliminating those he saw as national competition. Why not wrap racist propaganda around his plan to focus his nation's fears into motivation to fight against what he pereceived as nationalistic competition.
Wiki extract:

"The master race (German: die Herrenrasse, das Herrenvolk (help·info)) was a concept adopted as Nazi ideology in which the Nordic peoples, one of the branches of what in the late-19th and early-20th century was called the Aryan race, represent an ideal and "pure race" that was the purest representation of the original racial stock of those who were then called the Proto-Aryans,[1] themselves believed by the Nazis to have prehistorically dwelt on the North German Plain and ultimately to have originated from Atlantis.[2] The Nazis declared that the Nordics (i.e., the Germanic peoples) were the true Aryans because they claimed that they were more "pure" (less racially mixed with non-native Indo-European peoples) than other people of what were then called the Aryan peoples (now generally called the Indo-European peoples), such as the Slavic peoples, the Romance peoples, the Iranian peoples, and the Indo-Aryans.[3] Claiming that the Nordic peoples were superior to all other races, the Nazis believed they were entitled to world domination.[3] This concept is called Nordicism."

I am of the belief that, slavic peoples were those who mostly live in the Balkans, through to the north western region of the Black sea. This might place a different emphasis on the answer.

I don't know what really Hitler's objection were.
But 'they' (= the leading Nazis, especially Himmler) regarded some as quite good, others as worse.

But generally, Slavs were seen as a racially inferior group,

Throughout early European history, Germanic tribes were in competition with Slavic ones in Eastern Europe.

We know from history that the Germans had a reputation for their farming skills. When they moved into an area and brought it under their heavy oxen driven plow, they were usually there to stay. Their food surpluses led to their rapid increase. Not only did German population increase, but markets and towns soon sprang up where dense forests and swamps had previously existed. Germanic settlers took credit for the trimming of the forests and draining of the swamplands of Pomerania, Prussia and Silesia; lands which were previously occupied by nomadic Slavic tribes. And many of these ancient Slavic tribes became integrated into the expanding German Reich, such as the Sorbs and the Wends who still live peaceably within modern Germany.

Eventually, as the numbers of Germans in previously Slavic areas increased, and it often came into armed conflict. The Germans believed that they had the greater moral right to these eastern lands, which they refered to as their "Ostmark", because they claimed to be the first to make the land suitable for the plow and settlement. The work "Mark" is an ancient form of the modern word "March" and litteraly meant "Forward Outpost" or "Colony". The German "Ostmark" was spread all accross Eastern Europe and included, in addition to West Prussia and Silesia, sizable settlements in Bohemia, Moravia, Transylvania, (Siebenbürgen), and the Carpathians; the Buchovina and Banat were all famous for their considerable German presence and agra-markets. Last but not least; the great German colony known as the "Volga Republik" of Southern Russia, where the German polulation had once been numbered in the millions. These were not just ethnic colonies, they were productive markets which spead wealth all about them.

So the "expert" German farmers felt superior to their Slavic neighbors because they saw so much of the land under Slavic control and within the Slavic realm as not being very productively used. Today the Slavs, especially the Poles, say the Germans intruded upon ancient Slavic land, and the Germans reply that they took the land the Slavs were not using and made it productive for all. In most cases, the Slavs were glad to have German farmers within their midsts and the two cultures lived side by side in peace.
This is the jist of the centuries long historic conflict between Slavs and Germans in Eastern Europe.

By the time Hitler came to power, it had become a long tradition for Germans to "look to the east" for new lands to settle and this term oftem pops up in his speaches. A sizable chapter of Mein Kampf is also devoted to the concept of German expansion into Eastern Europe.