When you use "arrive home" or "arrive here," "home" and "here" are not nouns; they are adverbs, so you needn't use a preposition after "arrive".

You' re right, "arrive" is intransitive. By "intransitive," it just means that the verb does not take a direct object (which is always a noun or pronoun.) In your examples, neither "here" nor "home" is being used as a direct object of "to arrive." First, "here" is not a noun. While "home" is indeed a noun, just think of it as an "adverb" in the set expression "to arrive home" because like "here," it answers "to arrive WHERE?" Note also that there is no other noun in the English language which can be used without a preposition in "to arrive X." You *CANNOT* say "I arrived school," "I arrived work," "I arrived church." Home, I suppose, is such an important place that we've dropped the preposition "at" in the expression "to arrive home."

wut theus the wold got to bo with us

You' re right, "arrive" is intransitive. By "intransitive," it just means that the verb does not take a direct object (which is always a noun or pronoun.) In your examples, neither "here" nor "home" is being used as a direct object of "to arrive." First, "here" is not a noun. While "home" is indeed a noun, just think of it as an "adverb" in the set expression "to arrive home" because like "here," it answers "to arrive WHERE?" Note also that there is no other noun in the English language which can be used without a preposition in "to arrive X." You *CANNOT* say "I arrived school," "I arrived work," "I arrived church." Home, I suppose, is such an important place that we've dropped the preposition "at" in the expression "to arrive home."