Argh... now I really got it backwards. What I meant to say was that one does not write "shes", one writes "her", and not "wes" but "our". And that does not apply to "it".
To summarize, comparison to other personal pronouns is irrelevant since "it" has a special combination of rules.
I'm not sure how "it" is special". Because its possessive ends in an s? So do "theirs", "hers", and "ours" (which I think are the ones you meant).
I think you're having a hard time because you're overcomplicating the matter. "its" is the possessive of "it". "it's" is a contraction of "it is". Possessives adjectives: My, Your, His, Her, Their, Its. Possessive pronouns: Mine, Yours, His, Her, Theirs, Its. You have four less to remember than with most languages :)
I'm not sure why you need to tell me I'm having a hard time. I don't feel like having a hard time with this issue. Also I'm not overcomplicating anything.
You said it yourself: you're not sure how "it" is special. I'm sorry, I cannot help you any further. Maybe others in this thread can.
To summarize, comparison to other personal pronouns is irrelevant since "it" has a special combination of rules.