YUROP

Because the 81 to 97% of voters of the other parties who made it in consider it unacceptable.

Dude because they’re literal Nazis

Because the actual party with the most votes categorically refused to work with them. Going inti a coalitiin with the 3rd placed SPD will still guarantee the CDU a majority in the Bundestag.

In parliamentary democracies, the "government" is the term used for the ruling party or coalition. Even more specifically, it's used for the Ministers. It's a more specific term than just referring to all elected representatives sitting in the parliament (the Bundestag, in the case of Germany, or maybe the Bundestag & Bundesrat). Comparing it to the American system, "government" is somewhat analogous to the "executive"—the President and Cabinet Secretaries—except that it's a fuzzy term and can also mean the non-ministerial members of parliament who are allied with the ministers.

So the AfD will not be a part of the Government because both the CDU/CSU and SPD have placed a cordon sanitaire around the AfD. They refuse to work with them because they view them as dangerous extremists. It would be theoretically possible for the CDU/CSU to break that cordon and form a government between just their party and the AfD, or they can form a traffic light coalition with the SPD and Green party. The latter seems more likely, given recent German political history.

Cause they can't find common ground and form alliances with other parties, to form a majority.

At least that is how I understood it.