It’s seems like “it’s” SHOULD be the possessive, because so many possessives have apostrophes, but nope-- it ain’t so.
“The tree waved in the breeze, and the wind sang in ITS branches.” This is correct.
“It’s,” on the other hand, is a contraction for “it is.” The apostrophe takes the place of the letter “i” in “is,” just like the apostrophe takes the place of “o” in “don’t,” (do not) and “a” in “you’re” (you are).
I see this mistake everywhere, although, thank God, not so far in The New York Times (except in the reader comments section).
I believe it is the misuse of “it’s/its” that is the real cause of global warming. So, please, do your part for the ozone layer and get on board. Thank you.
This might be the wrong forum for this.