As per your expected output,

• Remove the not operator ! while calling the array in for loop.
• we don't require "Processing file" in that echo command.
• we don't need to pass the index value of array while looping it in for loop.

Try as

declare -a files=( "A1S0" "D1S0" "D2S0" "D3S0" "D4S0" "D5S0" "D6S0" )
command_to_get_filesizes() 
{
  for i in "${files[@]}"; do
    echo "$i"
  done
}
command_to_get_filesizes

As per your expected output,

• we don't require "Processing file" in that echo command.
• we don't need to pass the index value of array while looping it in for loop.

Try as

declare -a files=( "A1S0" "D1S0" "D2S0" "D3S0" "D4S0" "D5S0" "D6S0" )
command_to_get_filesizes() 
{
  for i in "${files[@]}"; do
    echo "$i"
  done
}
command_to_get_filesizes