This phrase creates a visual image to describe something that doesn't fit in. Wearing a Halloween costume to a wedding would make you stand out like a sore thumb.
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Metaphorical Use
Metaphorically, it suggests awkwardness or not fitting into a social context. Being the only adult at the kids' table made him stick out like a sore thumb.
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Negative Connotation
Often implies an undesirable or unintended level of attention. He tried to blend in, but his accent made him stick out like a sore thumb.