Swami Vivekananda said that Advaita, Vishistadvaita and Dvaita--all these doctrines are correct.
What did He mean by saying this?
Because Swami Vivekananda considered them as three steps in Spiritual progress. First step is Dvaita (dualism), second step VisistAdvaita (qualified non-dualism) and third step is Advaita (non-dualism) (final state of experience). He also said all three complement each other but do not oppose.
Swami Vivekananda says the following in Vedanta Philosophy - Volume 1 of Complete works.
The Vedanta philosophy, as it is generally called at the present day, really comprises all the various sects that now exist in India. Thus there have been various interpretations, and to my mind they have been progressive, beginning with the dualistic or Dvaita and ending with the non-dualistic or Advaita.
Swami Vivekananda answers the following when he was asked about relationship between Advaita and Dvaita, (from Volume 5).
Q.—Is the Advaita antagonistic to dualism?
A. —The Upanishads not being in a systematised form, it was easy for philosophers to take up texts when they liked to form a system. The Upanishads had always to be taken, else there would be no basis. Yet we find all the different schools of thought in the Upanishads. Our solution is that the Advaita is not antagonistic to the Dvaita (dualism). We say the latter is only one of three steps. Religion always takes three steps. The first is dualism. Then man gets to a higher state, partial non-dualism. And at last he finds he is one with the universe. Therefore the three do not contradict but fulfil.
He also says only through practice we can know which is true. He says the following in Volume 6.
Buddha came to whip us into practice. Be good, destroy the passions. Then you will know for yourself whether Dvaita or Advaita philosophy is true— whether there is one or there are more than one.
Swami Vivekananda explains his understanding in more detail in letter to Alasinga in Volume 5.
Now I will tell you my discovery. All of religion is contained in the Vedanta, that is, in the three stages of the Vedanta philosophy, the Dvaita, Vishishtâdvaita and Advaita; one comes after the other. These are the three stages of spiritual growth in man. Each one is necessary. This is the essential of religion: the Vedanta, applied to the various ethnic customs and creeds of India, is Hinduism. The first stage, i.e. Dvaita, applied to the ideas of the ethnic groups of Europe, is Christianity; as applied to the Semitic groups, Mohammedanism. The Advaita, as applied in its Yoga-perception form, is Buddhism etc.
Now by religion is meant the Vedanta; the applications must vary according to the different needs, surroundings, and other circumstances of different nations. You will find that although the philosophy is the same, the Shâktas, Shaivas, etc. apply it each to their own special cult and forms. Now, in your journal write article after article on these three systems, showing their harmony as one following after the other, and at the same time keeping off the ceremonial forms altogether. That is, preach the philosophy, the spiritual part, and let people suit it to their own forms. I wish to write a book on this subject, therefore I wanted the three Bhashyas; but only one volume of the Ramanuja (Bhashya) has reached me as yet.