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.
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 :)