Why activity class should (usually) be Public class?

It needs to be public, because your activity class does need to be accessed from another package. You have to realise that your app is not running in isolation on the system. In fact your app is not even a stand alone program - it has no main() method right? The app code is run by the Android app management system, which calls methods on your code - such as onCreate(). Therefore this code has to be accessible.

However there is no danger of other apps accessing your code, because the class loader doesn't allow it. Each app effectively has its own classpath, which is used to dynamically load classes.
Say for example my app had package name

A.B.myapp

and some other app was installed on the system with package name

C.D.otherapp

There is no way that myapp could load classes from C.D.otherapp (even if it did know the package name) because the class loader prevents it. If an attempt like that was made, myapp would get a ClassdefNotFound exception.