This is the idea that when a core belief is challenged then people double down on their beliefs and believe even more firmly in it than they did before they were challenged. This is often evident when trying discuss religion with creationists. Despite all the evidence that the earth is older than 6,000 years old they are completely entrenched in their beliefs.
Anybody who has tried to debate something online will recognise this immediately. Many people advocate for a change in tone when discussing ideas, such as trying to steer things towards personal stories and experiences, rather than hitting people with the numbers first. Arguably this isn't achievable with every topic, and what works for one person may not work for another.