In many philosophical works and ideas*, it seems like the number 3 gets a major, unexplained emphasis (mostly as a trichotomy).
One of the major ideas that uses trichotomy is the Thesis-Antithesis-Synthesis method of deduction:
provide thesis (a)
give it a contradiction by antithesis (b)
unite/solve the contradiction of (a) and (b) through a "higher" synthesis (c)
Here we see 3 parts of a solution; and using this 3-part solution the philosophers start building many many systems.
For example Schelling in the "First Outline of a System of the Philosophy of Nature" gives an explanation to planetary formation using gravity by postulating that for every 2 opposing masses there is a "higher", uniting mass (which is double the size of the opposing masses) that keeps the opposing masses from becoming one (thus destroying one of the planets); the third mass being usually a sun.
There is, though, many other ideas in philosophy that uses trichotomy, and the division to three.
For example Kant's categories: for each class of categories (Quantity, Quality, Relation and Modality) there are 3 categories derived by 3 types of judgements. You can also note, perhaps by chance, perhaps deliberately, that Kant divided his Critiques to 3.
There are many other examples, ranging from Plato to 20th century philosophers (thanks for @Conifold for the citation in the comments: trichotomy in philosophy).
What I'd like to ask is:
A. Is there a clear explanation as to why philosophers so often incline to a 3-part division? Is there an aesthetic reason here?
B. Can you please provide critics of this method of thought? What are the most popular criticisms? [Edit: most of the answers attempt to answer A, but none have tried answering B, which is equally important to me.]
*The original version of this question emphasized German idealism; I've corrected it according to Conifold that the trichotomy is a theme that runs throughout all of history. I still think that the Germans emphasized this number more than the rest, but it could be my own biased reading.