False. Not all tests should be automated.
This may seem like a very controversial statement at first but the truth is that some tests should remain manual. Blanket statements like "automate everything" are not based on analytics and do not demonstrate an engineering mindset. Even worse, these one-size-fits-all statements could demonstrate that decision makers are acting more emotionally than logically.
Companies have limited resources. This includes people, time, and money. Automation efforts need to reflect this reality.
A better approach is to come up with criteria for determining which tests should be considered eligible for automation. A scoring or prioritization process can be implemented to determine priority. If needed, this process can be cyclical (think sprints or spirals!) and repeated as often as necessary. This ensures that the process is adding value and improving software quality immediately.