Arguments against "initialize()" method instead of constructors

Both single step (constructor) initialisation and two step (with an init method) initialisation are useful patterns. Personally I feel that excluding either is a mistake, although if your conventions prohibit use of exceptions entirely then you prohibit single step initialisation for constructors that can fail.

In general I prefer single step initialisation because this means that your objects can have stronger invariants. I only use two step initialisation when I consider it meaningful or useful for an object to be able to exist in an "uninitialised" state.

With two step initialisation it is valid for your object to be in an uninitialised state - so every method that works with the object needs to be aware of and correctly handle the fact that it might be in an uninitialised state. This is analogous to working with pointers, where it is poor form to assume that a pointer is not NULL. Conversely, if you do all your initialisation in your constructor and fail with exceptions than you can add 'the object is always initialised' to your list of invariants, and so it becomes easier and safer to make assumptions about the state of the object.

This is usually known as Two phase or Multiphase Initialization and it is particularly bad because once a constructor call has finished successfully, you should have a ready to use object, In this case you won't have a ready-to-use object.

I cannot help but stress more on the following:
Throwing an exception from constructor in case of failure is the best and the only concise way of handling object construction failures.