Ubuntu – Copy every file in a directory structure into specific path only if file does not exist there already

find returns the root path because it matches your criteria—i.e. it is a directory, and it doesn't start with _.

You're looking for -mindepth 1, I suspect:

$ cd /tmp
$ mkdir a
$ touch a/b
$ mkdir a/c
$ touch a/c/d
$ find a
a
a/b
a/c
a/c/d
$ find a -mindepth 1
a/b
a/c
a/c/d

Reference: find manpage

If one really really really needs to have custom cp with custom message, then recompiling the program from source is the way to go, but a bit more sensible approach would be to write out your own message via printf preferably, instead of trying to intercept cp's output, and handle user choices via select dialog. Additionally, if you're going to output error messages, they should go to stderr stream. Finally, *.* is unnecessary and you can just use * glob instead.

Below is the script with a couple edits. Note that you need to uncomment #cp "$item" "$HOMEWORKDIRECTORY" line for the actual copying to occur. For testing purposes replace cp with echo first.

#!/bin/bash

USAGE="Usage: ./script2.sh [hw-name]"
EINVALID="Invalid homework: $1"
SOURCEDIRECTORY="$PUBLIC/homework/$1"
HOMEWORKDIRECTORY="$HOME/homework/$1"
#COPY="$SOURCEDIRECTORY/*.*"

if [ -z "$1" ]; then
    echo "$USAGE" > /dev/stderr
    exit 1
fi

if [ ! -d "$SOURCEDIRECTORY" ]; then
    echo "$EINVALID" > /dev/stderr
    exit 2
fi

if [ ! -d "$HOMEWORKDIRECTORY" ]; then
    echo "making homework1"
    mkdir -p $HOMEWORKDIRECTORY

for item in "$SOURCEDIRECTORY"/*; do
    skip=true
    if [ -f "$HOMEWORKDIRECTORY"/"${item##*/}" ]; then
        printf "%s already exists in %s.\n" "$item" "$HOMEWORKDIRECTORY"

        select choice in  "overwrite" "skip"; do
            case "$choice" in 
                "overwrite")  echo "Overwriting."  
                              break;;
                "skip") skip=true; break;;
            esac
        done
    fi

    if [ "$skip" = "true" ]; then
        continue
    fi
    echo cp "$item" "$HOMEWORKDIRECTORY"

done