This is based on M Oehm's idea and J. Siebeneichler and Bass's comments; I only contributed
but since the answer hasn't been posted yet let's put it up!
... As M Oehm thought, each line corresponds to a letter (most of this is quoted from their answer):
• I watch — C: I see
• I salute — A: as in, "hey!", or "ay!" (J.Siebeneichler suggestion)
• I am multiple — R: "I am" multiple is "we are"
• I am myself — I: literally I
• I sting — B: a bee stings
• I dig — O:
a circular hole, or I dig=I love=>love in tennis=0 => O (Bass suggestion) a hoe!
• I am yourself: U: you yourself
• I was: — X: it is an ex-parrot, it was but is no more
• I question: Y: the question is why
It is indeed
a Caribou, of the male persuasion,
cannot be milked.
Unless you join J. Siebeneichler's mind in the gutter of course! And who didn't.