There is a scholarly consensus that there is a Dravidian family of languages that is distinct from the Aryan family, and that Tamil is the closest to being the proto-Dravidian language.
The first extant Kannada text is the Halmidi inscription that dates to 450 AD; the first non-inscriptional text is Kavirajamarga, which by the most conservative estimate can't be dated to earlier than the 8th century.
Therefore in terms of antiquity Tamil is far older. Its inscriptions date to the 3rd century BC, while literary texts go back to about the 1st century BC.
Tamil is considerably independent from Sanskrit in its vocabulary, grammar and literary tradition—important criteria for consideration as a classical language.
In contrast there is a scholarly consensus that Kannada literature's largely derivative and owes a considerable debt to Sanskrit.
Finally, the government's recognition of Tamil as a classical language is only a fait accompli as Tamil already enjoys the status of a classical language in advanced centres of research and universities across the world.