The bird's neighbours are the other birds and creatures that live in the same tree and the trees nearby — sparrows, parrots, crows, squirrels, and the grown-up birds that hatched before it.
Two clues point to this. First, the bird has spent its whole life in one tree, so ‘neighbours’ must mean the ones sharing that tree. Second, the line is “I don't know how the world is made, / And neither do my neighbours” — it compares itself with them as equals, which only makes sense if they are creatures like itself.
A second reading is also defensible, and worth mentioning in the discussion: the poem is really about all of us, so the ‘neighbours’ may stand for everyone else in the world, human beings included. Read that way, the last line says that no one — bird or person — fully understands how the world is made. That is the stronger and more interesting reading, because it turns a small poem about a chick into a poem about growing up.
How to answer a ‘why do you think so’ question: Give your answer, then quote or paraphrase the line that supports it. Never leave the ‘why’ half unanswered.