To become "unschooled" a character needs to be under 28 and dull, uncharismatic and lazy:

Code:
Trigger Unschooled_Low_Intelligence_and_Lazy
  WhenToTest CharacterTurnEnd

    Condition AgentType = family
          and Trait NaturalIntelligence < 3
          and Trait NaturalEnergy < 4
          and Trait NaturalCharisma < 3
          and Trait Unschooled < 1
          and Trait TurnsAlive < 3

  Affects Unschooled  1  Chance  5
Men of the Hour are more likely to be unschooled:

Code:
Trigger Practical_Self_taught_ManOfHour
  WhenToTest LesserGeneralOfferedForAdoption

    Condition AgentType = family
          and Trait NaturalIntelligence > 4
          and Trait NaturalEnergy > 4
          and Trait Unschooled < 1
          and not Trait Scholarly > 0

  Affects Unschooled  2  Chance  25
so are characters of the following people:

Ptolemaioi Aigyptios
Getai Bessos
Iberia Celtiberi
Iberia Vettones
Iberia Vaccei
Epeiros Chaon
Epeiros Thesprotos
Epeiros Molossos
Epeiros Liburnos
Baktria Persikos
KH Kres
Casse Cruithni
Arverni Cruithni
Aedui Cruithni

Beeing unschooled might lead to become a "self taught man" with these possible benefits:

Rhetoric Skill
Philosophy Skill
NaturalPhilosophy Skill
Architect Skill
Good Engineer
Good Administrator
Logistical Skill
Tactical Skill
Politics Skill
Pragmatic
Mathematics Skill