Why island and not light? There are some phrases in the suttas where it is said "be your own island".

The word for "island" is "dvipa" in Sanskrit, meanwhile "dipa" means "light" or "lamp" in Sanskrit. However, in Pali, "dipa" means both "island" and "light" / "lamp". Due to this, it is quite common for the phrase to be mistaken as "be your own light", especially among speakers of Indian languages.

Why does the sutta say "be your own island" instead of "be your own light"?

What is the significance of "be your own island"?

From SN 22.43 (translated by Bhikkhu Sujato):


  “Mendicants, be your own island, your own refuge, with no other
  refuge. Let the teaching be your island and your refuge, with no other
  refuge.
  
  Attadīpā, bhikkhave, viharatha attasaraṇā anaññasaraṇā, dhammadīpā
  dhammasaraṇā anaññasaraṇā.


From this footnote by Maurice O'Connell Walshe:


  Atta-diipaa. Diipa means both "island" (Sanskrit dviipa) and "lamp" (Sanskrit diipa), but the meaning "island" is
  well-established here. The "self" referred to is of course the
  unmetaphysical pronoun "oneself"
There's a footnote in What the Buddha Taught by Walpola Sri Rahula:


  Dipa here does not mean lamp, but it definitely means 'island'. The Digha-nikaya
  Commentary (DA Colombo ed. p. 380), commenting on the word dipa here says:
  Mahasamuddagatam dipam viya attanam dipam patit/ham katvd viharatha. 'Dwell making
  yourselves an island, a support (resting place) even as an island in the great ocean.'
  Samsdra, the continuity of existence, is usually compared to an ocean, samsarasdgara, and what is required in the ocean for safety is an island, a solid land, and not
  a lamp.