The noun 'dad' is a common noun, a general word for a male parent; a word for any dad of anyone.
A common noun is capitalized only when it's the first word in a sentence.
A proper noun is the name or title of a specific person, place, or thing. When the male parent is your dad, you call him 'Dad' which is a proper noun as his title. As a proper noun is always capitalized.
Examples:
Jack's dad will pick us up. (common noun)
I made lunch for you, Dad. (proper noun)
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