I went there for having fun

A student from Brazil taught us definitions from his field, Public Policy Administration. He explained, "A policy needs to change for a new policy." I corrected him that "change to" is what he meant. "TO" is direction towards: "I am married TO John, divorced FROM Vladimir." "For" is a purpose, why we do something. "I wrote a letter TO Jack FOR Jill since her hand was broken."
This lead to another problem Spanish and Portugese speakers have. They often use a gerund after a preposition, which makes sense since prepositions are followed by nouns. However, it is awkward to follow them with gerunds. "I went there for having fun." "I went there for fun OR to have fun" (the infinitive is a reduced form of in order to.) I don't know why gerunds don't work. We use them after prepositions in other constructions. "I am good at swimming." "I look forward to meeting your mom."
After FOR seems okay in this question: "How much money do you get for teaching part-time?" Maybe it doesn't. Maybe I'm losing my ability for judging the English.