Selective retention

Selective retention, in relating to the mind, is the process whereby people more accurately remember messages that are closer to their interests, values and beliefs, than those that are in contrast with their values and beliefs, selecting what to keep in the memory, narrowing the information flow.

Examples include:

Outside of the theory of memory and mind, selective retention may also refer to the retaining of contractual agreements upon moving on in open politics or of physical phenotypes in eugenic methods of propagation of traits and features of a genome, among other fields where action can impose a stratum of creative limitation.

...
Wikipedia