There are still people who dictate their emails to a secretary.
Technology changes, people often don't.
Programmers will be around for a longer time than anyone realises because most people don't understand how the magic box works let alone the arcane magics that run on it.
Yes, it is an easy sell. But when that happens this sentence will also be viable - "We can remove the need for your company, valued at multiple millions a month" ... because after all, PMs and CEOs aren't harder to replace than programmers at that point.
Technology changes, people often don't.
Programmers will be around for a longer time than anyone realises because most people don't understand how the magic box works let alone the arcane magics that run on it.