So why do some Hindus believe that a person dies and that spirit part of them, whatever that is called, is put into a different body on Earth? What Scriptures do they use to come up with those beliefs? Since Baha'is don't believe that, then how are those Hindus wrong?
Then, how are Baha'is right in saying that a body dies and goes on to a higher plane, and that only the "qualities" of a person returns?
I can't answer that for you. I only know the Bhagavad Gita well, and have not read that for a while. The Hindus, if you ask them, will show you the scriptures that leads them to believe what they do.
The only thing I can say right on behalf of Baha'is now is that those scriptures are unreliable to show what Krishna said, and no other source but what Krishna said in the first place is considered reliable truth. Here's some stuff on reincarnation from the Baha'i Writings:
“The Bahá'í view of ‘reincarnation’ is essentially different from the Hindu conception. The Bahá'ís believe in the attributes and qualities, but maintain that the essence or the reality of things cannot be made to return. Every being keeps its own individuality, but some of his qualities can be transmitted. The doctrine of metempsychosis upheld by the Hindus is fallacious.” (to an individual believer, March 27, 1938
Some of our qualities can be transmitted to another person who is born later, I think he is saying.
“Evolution in the life of the individual starts with the formation of the human embryo and passes through various stages, and even continues after death in another form. The human spirit is capable of infinite development. … [A human being] does not pre-exist in any form before coming into this world.” (to an individual believer, Nov. 26, 1939)
He passes into another form, but this form is not a
physical body.
“We know from His Teachings that Reincarnation does not exist. We come on to this planet once only. Our life here is like the baby in the womb of its mother, which develops in that state what is necessary for its entire life after it is born. The same is true of us. Spiritually we must develop here what we will require for the life after death. In that future life, God, through His Mercy, can help us to evolve characteristics which we neglected to develop while we were on this earthly plane. It is not necessary for us to come back and be born into another body in order to advance spiritually and grow closer to God."
“This is the Bahá'í Teaching, and this is what the followers of Bahá’u’lláh must accept, regardless of what experiences other people may feel they have. You yourself surely know that modern psychology has taught that the capacity of the human mind for believing what it imagines, is almost infinite. Because people think they have a certain type of experience, think they remember something of a previous life, does not mean they actually had the experience, or existed previously. The power of their mind would be quite sufficient to make them believe firmly such as thing had happened.” [ibid]