I have never heard of "tea breath".... probably because tea drinking does not cause bad breath. Coffee's association with halitosis is a disadvantage relative to tea's breath-neutral properties.
The cause of "coffee breath"
Volatile sulfur compounds accumulate in the mouth after drinking coffee, which causes a strong, pungent smell, often compared to garlic or rotten eggs.
Tea has very small amounts of volatile sulfur compounds. Tea has the added benefit of polyphenols with antimicrobial and deodorizing properties.
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