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Professor Oak is actual Ash's dad.
The reason for them never revealing it was that Ash was Oak's child out of wedlock.
He had an affair with Ash's mother and later she got pregnant.
Because at the time Oaks was already married they decided to keep their affair secret because they didn't want to destroy Oak's reputation and also disturb the peace of his legal family.
They both consented to that and to this day they are still devoted to each other.
Ash didn't inherit Oak's brains but luckily he inherited his passion for Pokemon so that alone allowed him to become a world champion so the genes are still strong and both Oak and his mother support their son.
