Its is a pronoun, like his and hers. You wouldn't write "Frank and I walked down the road and I held hi's hand." Its / it's is completely consistent.
Well yeah, that's the rule. That possessive pronouns don't have the possessive apostrophe that proper nouns would have.
I think it's a strange fluke. If I designed the language, I would use the form common to the plural apostrophe for possessive pronouns.
I held its' hand.
I held his' hand.
I held her' hand.
This would allow the contraction to use the apostrophe and possession to use the apostrophe, always. Since the plural of "its" is a different word, "their", same with his and her, the plural form of the apostrophe is by nature impossible. Multiple "them" possessive is still them, so
their'
also is unambiguous without introduction a new exception to the rule ( like the current exception that pronouns don't need possessive apostrophe), it just expands the rule to its logical conclusion.
This is much simpler, and I guess as a programmer it's attractive to have a standard syntax.
My apostrophe rules are akin to "assignments always use the = operator" whereas the current rules in English are "assignments always use the = operator unless you are assigning a pointer, then no operator is needed." It's madness!
Anyway, the point of my post was that as part of a society with other people we agree to abide by certain rules and customs. These include the language we use to communicate, or even moral customs like being able to back up our claims, or not saying one thing and doing the opposite, etc. etc. So no matter how much I wish the apostrophe worked consistently (as I've described above), it doesn't, I'm not going to pretend it does, and I'm not going to force others to accept my rules when they aren't the common already-accepted ones by society at large.
I also have great disdain with including punctuation within quotes, even when the punctuation is not part of the quoted subject matter. Like:
Did you hear him say, "I like dogs?"
It's ambiguous if I am asking if you heard him ask the question "I like dogs" or make the statement "I like dogs." If we doubled-up the punctuation like:
Did you hear him say, "I like dogs." ?
or
Did you hear him say, "I like dogs?" ?
Would clear up the ambiguity. You'll see me do this sometimes, but it's really for me and I don't expect that others should follow me or they are [insert general group with negative connotation here].
