Although boob is indeed a common slang term for a woman’s breast, and televisions did indeed formerly have tubes in them, these do not not appear to have served as the basis for the term. Boob has also served as a common term for a foolish person for over a hundred years, and television has been referred to as ‘the tube’ since the 1950s. The two words were combined based on the notion that much of what is viewed on television is either foolish, or geared toward foolish people, also known as the booboisie, a word coined by HL Mencken for ‘the class composed of all who are considered boobs
Boob used to also mean stupid.
I’m boobies for boobies.