JOEL - You are partially right. It's the tannic acid that can
do some harm to our system that is found in black teas
and coffee.
But the caffeine is the ingredient that makes it
addictive(not the tannic acid) and makes people
continue to drink it thus subjecting them to more
tannic acid.
The First Presidency has said:
"the leaders of the Church have advised, and do now specifically advise, against the use of any drink containing harmful habit-forming drugs under circumstances that would result in the acquiring of the habit. Any beverage that contains ingredients that would be harmful to the body should be avoided." (1972 letter)
Caffeine is a "habit-forming drug" so we should avoid it for that reason as the leaders advise.
See this page.
And the tannic acid can be "harmful to the body" so we should avoid black teas and coffee for that reason as well.
Please read what I already said about this subject at this page which does mention the tannic acid
But ultimately the real reason we should not drink tea and coffee is out of obedience to God who has told us not to do it. (D&C 89)