Keyword “with sharing” runs in system mode then why keyword “without sharing” is introduced in Salesforce apex?

Without Sharing is reserved for cases where the User does not have access to the records, but there is a need to update them based on user input.

Use the without sharing keywords when declaring a class to ensure that the sharing rules for the current user are not enforced. For example, you may want to explicitly turn off sharing rule enforcement when a class acquires sharing rules when it is called from another class that is declared using with sharing.
public without sharing class noSharing {
// Code here

}

Thanks