Sacrifice drives my medicine,
but not in the sense you speak ...
in my tradition sacrifice is personal -
hair, blood, fasting, deprivation, etc. -
a goat or sheep is not personal,
and so to 'sacrifice' an animal would be against my ethics.

Since ceremony is typically made out in Nature,
any 'remains' of a sacrifice are gifted to the ceremony site ...

If we are offering something to the Spirits, Ancestors or Gods
do we know what they really want or do we even have access to it?
In my tradition one's life should be one's offering -
to that end we try to live it mindfully and selfishly...
it is the only way to glorify the Creator.

NHT

I have never understood how putting flowers
(ie killing them to bring them to the altar) makes sense

The key lies in balance and humility ...
the Green Kingdom often steps forward to help me -
not only as offerings but also as medicine -
Flowers in particular are most gentle, loving helpers -

When working with the Green Kingdom
it is important to offer thanks for their selfless willingness ...
additionally take care to not pick an entire family,
but to mindfully leave most of it in tact -
I often wait for the elder of a group to designate
which family members are appropriate for any given task ...
in this way their family balance is not disrupted.

...the ancestor offering this advice would have sacrificed a goat or sheep in their time.  Perhaps it is the frame of reference which our ancestors have and what they are used to?
Might it be possible that our ancestors were much more aware than we are
of the interconnectedness between all living things -
so that as they made, say, an animal sacrifice,
the animal's suffering was their own?
In modern times, recognition of, and therefore empathy based on this interconnectedness has been lost ...