How can the inability to adapt may cause a species to become extinct

This is called Natural selection, if a species can not adapt to its in environment it will b come extinct because for example if you were to have a white mouse in a brown forest it would get eaten instead of having a brown mouse that has adapted, it would be able to survive

Not being able to adapt creates competition from those who can adapt, new predators and loss of habitats. Those are all environmental pressures that can limit the growth of a population and lead them to extinction if they are unable to adapt.