I never lived in paris, only went there a couple of times so what i will say is just my view + the reports i gathered from people i know and on the internet.
If you re visiting just to sight see for a couple of days, paris is beautiful (one of the most beautiful in the world in my eyes) and rich in history provided that you did some researches on the "no go zones" to avoid that makes paris a complet shithole overall imo, but usually the touristic parts are pretty safe, people that come with no plans can have a bad experience if they dont know where they go, wandering tourists are the perfect targets but you're from the us so i guess you're aware of that no disrespect.
Another thing that makes tourists "hate" paris is that it can be pretty dirty (accentuated by the stereotype) even though most capitals are not that must better on that aspect(london,rome...)
The "parisians are arrogant and cold people" from tourists usually comes from the fact that englando not great i guess,but if you make the effort to speak french, people will be mostly friendly, people always love when you show that you're interested in their culture if you can call a language being part of a culture.
If you're visiting to sight see AND embrace french culture and history, i assume you're visiting for at least a couple of weeks and have the will to travel around the country, just like i said there is something to see at every corner and is completly different in each parts, brittany, mont saint michel in normandie, les chateaux de la loire, beaches in the south, corsica, mountains in the alpes, the german/french marriage in the east, teh countryside in the center and much more...(train is pretty cheap and will get you anywhere + trains are cool :) )
As for why frenchies hate parisians, i would say its because paris="arrogant" rich people or poor shithole no go zones, there is no middle class, or because of football rivaleries, im not sure, i dont really hate parisians myself.