Saying "my body" implies an assumption of self, or you could say it's an expression of self-view. It doesn't seem all that conclusive to me.
Are you saying that atman is eternal and just "inhabits" our body while we're alive? Something like that?
Yes atma is
eternal and is atomic(paramAnu swaroopa, that which is not divisible) and is non-materialistic entity.
Sri Krushna says in BhagawadGita (Atma is I/we)
Atma(I) is never born, never dies, and is everlasting. Our body takes birth and dies, but not Atma. Atma supports the body. Without Atma, the body becomes dead. Atma supplies the energy to our body, mind, and senses which are
insentient and does not contain any knowledge. Weapons cannot cut Atma, fire cannot burn it, wind cannot dry it, and water cannot make it wet. Therefore, we should not grieve over death of the body because the Atma inside the body never dies.
(Gita 2.23-24)
Yes body is just a vehicle that we/atma travel in. Just like you live in the house but you are
not the house. When the physical body is dead, atma along with 5 Jnana indriyas(5 subtle senses) and manas(mind) transmigrates and occupies a
different body based on the karmic burden it carries. Atma/we is Pure and no
impurity can touch it. So you might question, how the karmic burden gets formed on atma? Karmic records or Karma samskAras are formed at various levels 1. Body 2. 5 senses 3. Manas(mind) and some others. Subtle senses and manas gets carried along with atma after death and these have the karmic records
which determine the next birth. This is one of the reasons the vedantins/vedics burn the body after death because karmic records will be written at body level also and when the jIva/atma/I go to a different body, these karmic records on the earlier body show effect on us.....When you become fully enlightened and erase all of the karmic records, these manas and 5 senses gets released from
atma and pure atma is liberated or attains liberation. What happens to atma after death of body and what place it goes is a BIG topic which I do not want to mention here. Also how atma depending on good virtues/bad virtues attain swargam(heaven) or naraka(hell) for brief amounts of time and on what paths and process again it falls down to earth to take a body is also a complex and vast subject. One might have a question here, atma needs a body to enjoy pleasures/pain in heaven/hell, so it is given a
Yaathana Shareera(different body) where it is subject to punishments/pleasures. One has to remember at this point, heaven/hell is just a temporary place in Sanatana dharma, one who goes to heaven/hell has to fall back to earth where he is subjected to same process. The concept of atma/soul(a corrupted word) across the world comes from
Vedam because it is the primary source which mentioned it in first place. Last point is atma is also called as jIva and jIva/we is not a male/female. Male or female is only due to karma.
Also
@Windwalker yes body is important only because it is only the source through which we/I could attain liberation/mOksham. It has to be cared for and treated good, my point was more inclined to people who follow a rigorous practice called Átma sAkshAtkAram. These people are called Jnana Yogis and they don't care for the bodily pleasures and their focus is always directed inwards.