It’s a right wing talking point, based on this quote from the BLM organization (directly from their website):
We disrupt the Western-prescribed nuclear family structure requirement by supporting each other as extended families and “villages” that collectively care for one another, especially our children, to the degree that mothers, parents, and children are comfortable.
First of all, this quote says nothing about “destroying”. Personally, the idea of caring for children in your community as if they are your own family sounds beautiful.
Second of all, if this alone is what sways you away from Black lives mattering, then you clearly were not strongly on that side in the first place. You’re simply looking for an excuse to discredit BLM.