A person who catechizes; someone who teaches others by asking questions and requiring them to answer from memory.
From 'catechize' plus the agent suffix '-er' (one who does), giving 'one who catechizes.' The role was especially important in early Christian education and religious instruction.
A catechizer was basically a human quiz machine—often a priest or educated lay person whose job was to drill biblical knowledge into congregants before the era of schools, making them crucial figures in spreading literacy and religious understanding.
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