You say 'I like to do something' or 'I like doing something' to refer to something in general, as in "I like to watch movies." or "I like watching movies." Can you use like in more specific situations showing some kind of intention as in "I like to watch the/this movie."
Does the sentence "She doesn't like to admit she's wrong." refer to a general or a specific situation? Is it that she generally doesn't like to admit she's wrong, or that in a specific time and place she is refuring to accept she's wrong?