Analysis of Puppy And I

I met a Man as I went walking:
We got talking,
Man and I.
'Where are you going to, Man?' I said
  (I said to the Man as he went by).
'Down to the village, to get some bread.
  Will you come with me?' 'No, not I.'

I met a horse as I went walking;
We got talking,
Horse and I.
'Where are you going to, Horse, today?'
  (I said to the Horse as he went by).
'Down to the village to get some hay.
  Will you come with me?' 'No, not I.'

I met a Woman as I went walking;
We got talking,
Woman and I.
'Where are you going to, Woman, so early?'
  (I said to the Woman as she went by).
'Down to the village to get some barley.
  Will you come with me?' 'No, not I.'

I met some Rabbits as I went walking;
We got talking,
Rabbits and I.
'Where are you going in your brown fur coats?'
  (I said to the Rabbits as they went by).
'Down to the village to get some oats.
  Will you come with us?' 'No, not I.'

I met a Puppy as I went walking;
We got talking,
Puppy and I.
'Where are you going this nice fine day?'
  (I said to the Puppy as he went by).
'Up to the hills to roll and play.'
'I'll come with you, Puppy,' said I.