The reason why you might get a ConcurrentModificationException when you modify a collection while you're iterating over it, is because many iterators can't work reliably anymore when you change the underlying collection. Some iterators provide operations like add() and remove() (on the iterator, not on the collection) that allow safe modification of the collection without the iterator getting confused. If you use those, it will work.
Note that it depends on the implementation of the iterator and the collection class whether you get a ConcurrentModificationException or not - it's not guaranteed that you get that exception. The API documentation of ConcurrentModificationException explains it:
This exception may be thrown by methods that have detected concurrent modification of an object when such modification is not permissible.
For example, it is not generally permissible for one thread to modify a Collection while another thread is iterating over it. In general, the results of the iteration are undefined under these circumstances. Some Iterator implementations (including those of all the general purpose collection implementations provided by the JRE) may choose to throw this exception if this behavior is detected. Iterators that do this are known as fail-fast iterators, as they fail quickly and cleanly, rather that risking arbitrary, non-deterministic behavior at an undetermined time in the future.
This exception may be thrown if you try to modify your collection while you iterate over it. There are Collections like the CopyOnWriteArrayList that will not throw this exception. If the data structure allows you to change the collection contents during iteration then this exception will not be thrown.