Why does “ocupo” mean “I need” in Mexico?

Your dictionary says “ocupar” means “to occupy.” But in Mexico, “ocupo huevos” doesn’t mean “I occupy eggs” — it means “I need eggs,” a flat synonym for “necesito.” It works with nouns (“ocupo dinero”) and with verbs (“ocupo estudiar,” I need to study). Outside Mexico and Central America this sounds wrong, so a Spaniard or Argentine would hear only “I’m busy with eggs.”

The standard meanings still hold everywhere: “estoy ocupado” (I’m busy), “el cargo que ocupa” (the post he holds). The “need” sense is the regional layer stacked on top. If you want to be understood across all dialects, “necesitar” is always safe; “ocupar = necesitar” is the local color to recognize, not to export.