git_branch_parent.sh

#!/usr/bin/env zsh

branch=`git rev-parse --abbrev-ref HEAD`

git show-branch | ack '\*' | ack -v "$branch" | head -n1 | sed 's/.*\[\(.*\)\].*/\1/' | sed 's/[\^~].*//'

# How it works:
# 1| Display a textual history of all commits.
# 2| Ancestors of the current commit are indicated
#    by a star. Filter out everything else.
# 3| Ignore all the commits in the current branch.
# 4| The first result will be the nearest ancestor branch.
#    Ignore the other results.
# 5| Branch names are displayed [in brackets]. Ignore 
#    everything outside the brackets, and the brackets.
# 6| Sometimes the branch name will include a ~2 or ^1 to
#    indicate how many commits are between the referenced
#    commit and the branch tip. We don't care. Ignore them.

Doesn't latest git support showing the parent branch in a native way?

found the following to work for me (limited testing)
git branch --create-reflog | head -n 1