Even if a villager doesn't inherit skills from a parent, they will often "teach" themselves a skill. If you have a skill (say farming) checked for them as a child, when they turn 14 they will likely attempt to learn that skill.
Often, a villager will spontaneously teach him/her self a new skill if it fits their "likes." For example if a child's likes include wood, that child may teach himself building, even if you set him to farm.
Research seems to be the skill most villagers will default to without guidance, followed closely by farming.
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Fan Fiction MentorAvvie by Airstream Raider
Where have all the Fan Fiction Fans gone?
(I miss Laurence )
I miss my wife