I NEVER use apostrophes in possessives (unless the noun ends in "s,") for two reasons:

1) Consistency. Contrary to the practice of centuries, the style for several decades has been, as you know, to spell "its" (the possessive form of "it") with no apostrophe to avoid confusion with "it's" (the contraction of "it is".) I merely observe that practice with all nouns and pronouns rather than in a single anomalous pronoun.

2) The aforementioned practice is sometimes justified on the grounds apostrophes represent elided letters and that none are present in a possessive construction. This is not, strictly speaking, true, because the use of apostrophe plus "s" to form English possessives reflects English forming possessives in "es" about half a millennium ago. Custom gradually elided the "e" with an apostrophe so we use apostrophe plus "s" today despite most peoples ignorance of the cause. Few but language history scholars would now recognize "es" as possessive, and it is consequently quite justifiable to drop the apostrophe altogether for possessives.

In other words, it can be argued that an apostrophe has a rightful place in both "its" and "everyones" AND that it has no place in either, but arguing it belongs in one and not the other is untenably contradictory. As with "its" and "it's" context invariably makes quite clear whether "Mikes" means "the thing belonging to Mike" or "Mike is." So much so that I have consistently avoided apostrophes in forming possessives from the day I joined wotmania yet believe this may be the first time anyone has corrected me for it.