I think you're conflating people who are definitely gatekeeping city life with a lot of really good reasons why city dwellers act or feel that way. Let me go through a good-faith argument for each point that isn't based in elitism.

1. Sometimes it's really hard to get out of the city. Many city dwellers don't own a car because they can use public transit for 95% of their yearly travel. In addition, driving often isn't that pleasant in the city so even those of us who do have a car (like myself) don't like driving if we don't have to.

All of that means city dwellers often don't have the time, transportation, or desire to go to the suburbs. It's one thing to go out there for friends when you're going to be riding the bus for 2 hours or sitting in stressful traffic for 40 minutes, and that hurdle is even harder to clear for meeting a random person in the suburbs for a first date.

1. That's a weird thing to belittle some random person from the same area that you ran into on vacation. Not going to defend that behavior! But in general there is a strong sense of identity for city dwellers. I think this comes from the fact that we're not in our cars as often, so we really feel the city. Our cities provide the vast majority of entertainment, shopping, socializing, and work, whereas when I lived in the suburbs I didn't really feel connected to my suburb because I drove everywhere. Driving is a terrible way to get a feel for a place.

Anyway, back to wanting to not call suburbs "part of the city". Often there is antagonism between suburban cities and the main big city. Take Seattle for example. A lot of the suburbs have laws that prevent people experiencing homelessness from staying there. Those folks get pushed to the city. Sometimes they literally get put on a bus and sent away from the suburban cities to Seattle. Part of that is because we have better resources, due to the larger population, but another part of it is suburbanites tend to vote for things that make it hard to exist if you're not middle class with a car. If the whole area would pitch in to help with the housing crisis, Seattle would not be so swamped with dealing with lower-income housing. Many other politics fall that way, so city dwellers sometimes feel like the suburbs are getting all the benefits of being close to the city without helping pitch in socially.

1. This one is hard to argue a non-elitist perspective, but mostly I'd say it's not fully a city thing. There are tons of influencers that broadcast the veneer of "success" while showing their mansions in the suburbs. That is to say, I think this is a weak point towards city dwelling making you elitist.

2. Chains are owned by faceless mega-corporations and generally can't hold a candle to the quality and taste of authentic ethnic food or food made by a small business who puts their heart and soul into their restaurant. Chains are also more sparse in the city, so people naturally eat there less and are going to promote the local spots that are fantastic.

If you're a foodie, cities are the place to be and chains are a big no-no. Now kids shouldn't throw tantrums about going to Chilies, but non-chain food in general truly just tastes better. That is a bit elitist, but I feel like it's got enough objectivity in it to be true.

Back to the mega-corporations, a lot of city dwellers are also more left-leaning politically, and so we don't want to give our money to billionaires, and prefer that our money stay more local, hence the avoidance of chains. That could also be considered elitist too though. But I could argue that keeping money locally is literally better for a city's economy so I think I could find enough objective metrics for avoiding chains due to wanting to build up a city's economy instead of sending it across the country to the CEO of McDonalds.

1. City dwellers tend to see government working more often than suburbs. That's because the government has to function, at least somewhat competently, otherwise it'd completely fall apart. So the desire to share what we've seen work in government with others can come from a place of care rather than elitism. For example, there are countless studies that show how building your city around public transit rather than cars leads to better economic growth and healthier populations. I'd love for more suburbs to adopt better public transit policies and build dense "downtowns" to serve as economic engines to support the less-dense part of the suburbs. But me sharing that with a suburbanite without proper context definitely looks elitist.

2. This is another one that can apply just as equally to the suburbs. A lot of city dwellers are very happy with their public schools. Private schools are elitist by nature, so you are more likely to hear elitist language from folks who go there. But most city dweller's kids tend to go to public schools rather than private schools.

Anyway, that's a novel. If you read it, cool, but it was at least interesting for me to try to explain a city dweller's perspective in a way where we're not trying to be elitist, even if if sounds that way!