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I do not believe, "I like her/him" – Eu gosto dela/e – is possessive (though it can get that way) but de is the compulsory preposition for gostar which must contract with certain pronouns (he/his, she/her, here, that, this...).
On that note, em is the compulsory pronoun for pensar so de does not work with it.
I find prepositions to be the hardest part of learning any new language. Especially when they are associated with verbs. I struggled with this in French class, as a kid. There are even verbs that take a preposition in French but not in English (and vice versa). For instance, "I telephone Jack." vs. "Je téléphone à Jacques." Rather than thinking in him (Portuguese), in French, it is to (i.e. "Je pense à lui."). And in English, it is "about"...How is one to keep this all straight without moving to another country? (This is how I finally managed, with French.)