It’s because “home” in this formation is an adverb, whereas school is a noun. You can be an adverb- I’m surprised, I’m exhuasted… - but you must be at a noun (or on, or in, or some other preposition).
You're thinking in terms of location, rather than state-of-being. "I'm home" is your status.
"I'm driving, I am bored, I'm safe, I am away"... None of those sound weird, do they? This, combined with the more technical grammar rules others have commented...