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human
[Fullmetal Alchemist: Brotherhood] Why couldn't Edward and/or Alphonse transmute their bodies back just utilizing the elements and components?

To my understanding, the basic concept of equivalent exchange is that in alchemy, you reorganize base elements into new combinations/shapes/forms to create or change something. You pull the iron from the earth to make a weapon, you reform the molecules in a wall to make a door, etc. 

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Also, to my understanding, although the Elrics did have, to the best of their knowledge, every required material needed to create the average human (which would likely be more than enough to recreate what seemed to be a petite, short woman), the reason they are unable to resurrect her is both because her soul has left the mortal realm and is thus unattainable, and because there is no object that equals that value to be sacrificed for its gain, which causes the rebound. 

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But we know that alchemy on animals is possible, because chimeras are relatively commonplace, and even alchemy on humans in general is possible, because Shou Tucker creates a half/human chimera with his daughter. So, knowing that, why weren't the Elrics able to just transmute his arm and leg back with the elements and materials needed for the average 15 year old male arm and leg? To a limited extent, one might argue the same is possible for Alphonse, as his soul is already present and is naturally drawn to its human body anyways, meaning theoretically it would bond more securely with an alchemically created human body, similar to the ones created by the military.

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Basically, why do they need the damn stone in the first place?
gpt
They did investigate other methods, and found they were either unfeasible or not worth the cost.

Biological alchemy was one of the first methods they investigated, and it wasn't nearly advanced enough to be reliable. Shou Tucker, the leading expert in the science, was hitting a dead end over and over, to the point of losing his commission. The "bio-alchemy barrier" seems to have been crafting a living being from scratch; which is why creating a creature with something near human intelligence took a human base.

Tucker's technique would likely require human donors to create authentic-enough limbs and a full body. They weren't willing to do that, and even then, that wouldn't feel like *their* bodies, but bodies stolen from someone else.

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Human alchemy (as in, anything not done by Truth) may not have been able to restore their bodies in any case, since their loss was the result of human transmutation. Hohenheim didn't restore Izumi Curtis's organs, even with a Philosopher's Stone. It's a bit ambiguous whether he *wouldn't* because it was her earned punishment, or whether he actually *couldn't* because it was in God's domain - but it raises the possibility that humans can't restore parts taken by Truth without it facilitating an exchange.