I'm presuming this question is inspired by the Wiccan Rede and the quote "Elder is the Lady's Tree, burn it not or cursed ye be!" Unfortunately there is very little information available as to the origins of this and why There is a tentative tradition that witches allegedly used to have the power to transform themselves into elder trees so it is possible that the folklore started from this legend.
Christian tradition has it that Judas the traitor was hanged on an elder tree so this might explain the association with death.
I'm a practical witch and I believe that most folklore has its roots in practical answers. My guess would be that knowing elder is an unpleasant wood to burn, giving off little heat and a lot of quite smelly smoke it became a wood to avoid burning. I would imagine it was rejected as a source of firewood and the myths sprang from the reluctance of people to burn it. It is also a very quick burner so possibly there was a concern of the fire spreading too quickly for safety and this was also a factor in shunning it.
Elder is also a very useful tree with almost all parts of it having a purpose. The berries, the flowers and the leaves are all edible and even the bark can be used for medicinal cures. With elder trees providing so much bounty to the communities of old it is unsurprising that cutting them down for use of firewood was frowned upon.
Image http://www.sxc.hu/photo/1402779 (Ayla87)
Join the Witch Path Forward Facebook community. (Click the icon).
Changing your path/religion/way of life can be a time in your life when you need a bit of support. The purpose of this site is to offer a helping hand and a starting point to explore all the information available on the net.