Part 1

Historical revisionism is not a crime, anywhere. A certain number of countries outlaw Holocaust denial specifically and Holocaust denial is not revisionism. As per /u/Georgy_K_Zhukov in this post, Michael Shermer and Alex Grobman write that

For a long time we referred to the deniers by their own term of “revisionists” because we did not wish to engage them in a name-calling contest (in angry rebuttal they have called Holocaust historians “exterminationists,” “Holohoaxers,” “Holocaust lobbyists,” and assorted other names). [...] We have given this matter considerable thought—and even considered other terms, such as “minimalizers”—but decided that “deniers” is the most accurate and descriptive term for several reasons:

When historians talk about the “Holocaust,” what they mean on the most general level is that about six million Jews were killed in an intentional and systematic fashion by the Nazis using a number of different means, including gas chambers. According to this widely accepted definition of the Holocaust, so-called Holocaust revisionists are in effect denying the Holocaust, since they deny its three key components—the killing of six million, gas chambers, and intentionality. In an ad placed in college newspapers by Bradley Smith, one of the “revisionists” discussed in this book, he even uses this verb: “Revisionists deny that the German State had a policy to exterminate the Jewish people (or anyone else) by putting them to death in gas chambers or by killing them through abuse or neglect.”

Historians are the ones who should be described as revisionists. To receive a Ph.D. and become a professional historian, one must write an original work with research based on primary documents and new sources, reexamining or reinterpreting some historical event—in other words, revising knowledge about that event only. This is not to say, however, that revision is done for revision’s sake; it is done when new evidence or new interpretations call for a revision.

Historians have revised and continue to revise what we know about the Holocaust. But their revision entails refinement of detailed knowledge about events, rarely complete denial of the events themselves, and certainly not denial of the cumulation of events known as the Holocaust.

Holocaust deniers claim that there is a force field of dogma around the Holocaust—set up and run by the Jews themselves—shielding it from any change. Nothing could be further from the truth. Whether or not the public is aware of the academic debates that take place in any field of study, Holocaust scholars discuss and argue over any number of points as research continues. Deniers do know this. For example, they often cite the fact that Franciszek Piper, the head of the Department of Holocaust Studies at the Auschwitz-Birkenau State Museum, has refined the number killed at Auschwitz from four million to a little more than one million, arguing that this proves their case. But they fail to note that at the same time the numbers have been revised up—for example, the number of Jews murdered by the Einsatzgruppen during and after the invasion of the Soviet Union. The net result of the number of Jews killed— approximately six million—has not changed. In the case of Auschwitz and the other camps liberated by the Russians, since the end of the Second World War the Communists’ efforts to portray the Nazis in the worst light possible led them to exaggerate the number of the Nazis’ victims and the number of extermination camps. Scholars have had to clear through Communist propaganda to get to the truth about what happened. This sifting of data has resulted and will continue to result in Holocaust revision.

As far as the legal situation goes, at this point in time 16 countries outlawed Holocaust/genocide denial explicitly or implicitly (Austria, Belgium, Czech Republic, France, Germany, Hungary, Israel, Liechtenstein, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Romania, Slovakia, and Switzerland). Some of them like Austria of France do it explicitly in laws passed for this purpose, other do it implicitly by interpreting existing laws against hate speech, group libel, incitement to racial hatred or acts of racial or xenophobic nature in a way that outlaws Holocaust denial. The European Union decided in April 2007 to pass a law against Holocaust denial but leaves it to the members to incorporate it in their own law. (This coming from an unpublished article I wrote a couple of years back)

Obviously, some of this clashes with US American ideas of freedom of expression, so let me explain the legal situation.

TL;DR: European countries outlaw Holocaust denial directly or indirectly because as a form of political agitation, it poses a social and political thread to the established democratic order as well as to the social peace in these countries. Both are legal and historical sufficient reasons to outlaw this specific form of speech under the "pressing social need" exception, laid out by various constitutional courts and the European Human Rights court.

Freedom of speech is one of the most valuable freedoms in Europe. The European Human Rights Court found that “freedom of expression constitutes one of the essential foundations of a democratic society and one of the basic conditions for its progress and each individual’s self fulfillment.” Freedom of speech in Europe is guaranteed by the European Human Rights Convention, a Convention every member of the Council of Europe has to ratify as a condition to be member of the council. Currently every European country except Belarus but including Russia and Turkey is a member of the council. The European Human Rights Court can be invoked by every citizen of a signing state claiming a violation of rights guaranteed in the Convention by a court or another governmental institution.

Article 10 of the Convention protects freedom of speech, but also subjects it to the exceptions in the second paragraph:

1. Everyone has the right to freedom of expression. This right shall include freedom to hold opinions and to receive and impart information and ideas without interference by public authority and regardless of frontiers. This article shall not prevent States from requiring the licensing of broadcasting, television or cinema enterprises.

2. The exercise of these freedoms, since it carries with it duties and responsibilities, may be subject to such formalities, conditions, restrictions or penalties as are prescribed by law and are necessary in a democratic society, in the interests of national security, territorial integrity or public safety, for the prevention of disorder or crime, for the protection of health or morals, for the protection of the reputation or the rights of others, for preventing the disclosure of information received in confidence, or for maintaining the authority and impartiality of the judiciary.

The different approach to freedom of speech of Europe and the United States reveals itself regarding just the addressed subject of the legal text guaranteeing this freedom. While the First Amendment addresses the legislator as its subject prohibiting him to abridge the freedom of speech, Article 10 of the European Human Rights Commission addresses the citizen as its subject granting him the freedom of speech. The basic understanding is a different one: The First Amendment regards the legislator and government institutions as a “danger” to a freedom every citizen has. In contradiction to this, in Europe freedom of speech is something “granted” by the legislator to the citizen. The same legislator that “grants” a freedom is able to subject the same freedom to exceptions. The European Human Rights Court holds that these exceptions must be construed strictly. A pressing social need must exist to justify restrictions on the freedoms guaranteed in the Convention.

According to the European Human Rights Court, there is a pressing social need that justifies laws criminalizing Holocaust denial in various European countries such as France, Germany and Austria. Germany and France are examples of different legal ways nations within Europe chose to deal with the problem of Holocaust denial.