I have attempted to create an array consisting of two items: #0 and #1.
I am able to print the two items corrctly:

arr=(hello "my name is")
echo ${arr[0]}
hello
echo ${arr[1]}
my name is

for i in ${arr[*]}
do
echo $i
done

hello
my
name
is

hello
my name is

The problem is the behavior of the "for"-loop in connection with an obvious misunderstanding about what "${arr[*]}" means.

The subscript "*" in an array denotes ALL array elements and it is expanded before the for-loop is executed. Therefore this is what the shell "sees":

for i in ${arr[*]}            # original line, begin of parsing process
for i in hello my name is     # after expanding the variables

echo ${arr[*]} | while read a ; do
     echo $a
done

i=1
for i in {1..${#arr[*]}} ; do
     echo ${arr[$i]}
done

try also:

arr=(hello "my name is")

echo ${arr[0]}
echo ${arr[1]}

for i in "${arr[@]}"
do
  echo $i
done