They’ve been saying this since at least the first major use of the ATGM in the Yom Kippur War. It’s been nearly 50 years since then, and tanks are still around.
However, tanks are expensive to build, maintain, and operate, so as we see more inexpensive weapons that can kill them, we’re going to see less incentive to build or buy them.
Except what happened is Active Protection Systems, which are currently tipping the balance back towards the tank. NATO ignored APS for years, but recent events in Syria have NATO scrambling to bolt APS onto our tanks while Russia and Israel laugh and say “I told you so.”