The word Vishnu means (Vishwa(world)+ Anu(atom)), "One who is present in every atom of the universe/world". Thats why Vishnu is black in color. Black is formed when all the colors are mixed. The world is created on Triguna Mayi Maya Prakriti(Satva+Rajas+Tamas) and Vishnu(black in color) is the one who has accepted Prakriti and himself is the Prakriti involved in dynamic Rasa-leela of world, while Shiva(white in color) is the one who has rejected Prakriti completely and become static in Samadhi.
Its explained in Geeta, that
BG 4.6: Although I am unborn, the Lord of all living entities, and
have an imperishable nature, yet I appear in this world by virtue of
Yogmaya, my divine power.
Prakriti in itself is dead like a rope appears to be snake in a dark room. Its with the power of Purush i.e. cosmic consciousness that world appears to be moving. So, you cant say "I am Vishnu" because an individual soul has not created the universe, but the individual soul is same as pure cosmic consciousness "Shiva", hence "Shivoham". So, thats why Vaishnavas, prefer to consider themselves as white Radha and followers of Dwaita.
That which is Shyama is also Brahman. That which has form, again, is
without form. That which has attributes, again, has no attributes.
Brahman is Shakti; Shakti is Brahman. They are not two. These are only
two aspects, male and female, of the same Reality,
… Purusha and Prakriti. Whatever you perceive in the universe is the
outcome of this union. Take the image of Shiva and Kali. Kali stands
on the bosom of Shiva; Shiva lies on the ground like a corpse.
Prakriti performs all Her activities in conjunction with Purusha. Thus
She creates, preserves, and destroys. That is also the meaning of the
conjoined images of Radha and Krishna. On account of that union,
again, the images are slightly inclined toward each other.
To denote this union, Sri Krishna wears a pearl in His nose, Radha a
blue stone in Hers. Radha has a fair complexion, bright as the pearl.
Sri Krishna’s is blue. For this reason Radha wears the blue stone.
Further, Krishna’s apparel is yellow, and Radha’s blue.
All the gods like Surya, Laxmi etc., are extensions of Purush-Prakriti couple i.e. Shiva-Kaali(for introvert people) or Radha-Krishna(for extrovert people).
All are women, except He
Meerabai reached Mathura; there is one of the greatest temples of Krishna.
And the head priest of that temple had taken a vow that he would not
see any woman in his life; for thirty years he had not seen a woman.
No woman was allowed to enter into the temple and he had never left
When Meera reached there, she danced at the gate of the temple. The
guards became so enchanted, magnetized, that they forgot to prevent
her. She entered into the temple; she was the first woman after thirty
years to enter the temple.
The head priest was worshipping Krishna. When he saw Meera he could
not believe his eyes. He was mad. He shouted at her, “Get out of here!
Woman, get out of here! Don’t you know that no woman is allowed here?”
Meera laughed and said, “As far as I know, I know that except God
everybody is a woman — you too! After thirty years of worshipping
Krishna, do you think you are still a male?”
It opened the eyes of the head priest; he fell at the feet of Meera.
He said, “Nobody has said such a thing ever before, but I can see it,
I can feel it — it is the truth.”
Thats where Gyan and Bhakti split, the reason of conflict between Shaivas and Vaishnavas, non-dualistic Shaivas identify themselves with static Purusha while Dwaita Vaishnavas identify themselves with dynamic Prakriti. Both consider themselves, incapable of doing anything, as doer is Kaali/Krishna.