Thing is, it hasn't. Arabic spoken in the Maghreb is probably unintelligible to those that speak it in Syria. They call it Arabic, but in reality the languages are more than a bit diverged. If Dutch and Afrikaans are different languages then Arabic is long past that point.

To the Addendum: The Germanic tribes integrated linguistically because they were a minority trying to rule a majority that already had well-developed and sophisticated pre-existing structures that they were forced to use in order to control and govern the territory they made home.

The Slavs on the other hand, migrated in full force.Not just warriors but women as well.

The Arabs spread their language via a religion that was very lucrative to convert to so long as you were underneath Islamic rule; the languages of the people the Arabs conquered still exist in some of the outer edges of their former empire but for the longest time it was simply easier to switch to the language that was: the language of trade, of religion, of administration, of prestige. Arabic practically sold itself to everyone who wasn't too stubborn.

For the better part of their history, the Turkish controlled areas of Anatolia have had sizeable populations of Greeks. It's just with population exchanges, forced and unforced assimilation and lack of political leverage and presence that allowed Turkish to overtake Greeks in the lands that were once theirs. Also, much of the Arabic explanation applies to Turkish as well, at least in Anatolia.

The evolution in tandem of spoken and literary varieties of Arabic does offer a compelling analogy to the Latin example. But I would argue the result of that comparison is quite opposite to the one you present (i.e., the similarity is quite strong).

Like Latin, and arguably even more so, Arabic saw the continued use of a fairly static and thus geopolitically non-specific literary form of the language - Classical Arabic.

Furthermore, like Latin, and again arguably even more so, Arabic saw the dissemination of spoken registers throughout its empires, which acquired local vocabulary and features which rendered them very much distinct. Many came and went, as empires shifted. Some persisted.

Far from being cohesive, the family which included Cypriot Maronite Arabic, Maltese, Central Asian Arabic, Andalusian Arabic, Judeo-Arabic, etc., contains varieties with radically varied features, and various unrelated sources of new vocabulary (Latin, Greek, Hebrew, Uzbek, English), which layered themselves over the Arabic substratum.

The self-affirming aspect to your question, therefore, may be the implicit exclusion of various Arabic-descended languages from the category "Arabic" which you use. They are in effect excluded on the specific basis that they emerged as distinct languages, making the question effectively "of those Arabic-descended languages which are mutually intelligible, how did all of them persist in being mutually intelligible?" And as to answers on offer, there would be a few. But I would suggest a strong continued influence of Classical Arabic (supported by Islamic scholarship and jurisprudence), on the one hand, and the continued sociopolitical power of an Arabic-speaking ethnic Arabic population in the region, as another.