Anarchism is not anti-government. Anarchism is anti-hierarchy. Government is very possible without hierarchy, which is why most anarchists see direct democracy on the level of individual communities as the only valid system of government. One of the most popular forms of anarchism right now is anarcho-communism. One of the core ideas of anarcho-communism is that people need to band together as a free-association of producers society commune. It’s based on the ideas put forth by Kropotkin in The Conquest of Bread where his opening argument for anarchism is that everything that has ever been built has only been possible because of people cooperating and building off of each other.

It can sound a bit ridiculous at first because a lot of people spend their whole lives hearing nothing but anti-anarchist propaganda created by states that are inherently threatened by anarchism. If you’ve been told your whole life that anarchists are just weird people who hate the government then you’re probably going to end up believing it. Most anarchists I’ve met have held a negative view of anarchism at some point in their life because of it!

You should dig around the wikipedia page for anarchism a little bit. It might not convince you, but it does a decent job of presenting anarchist ideas as anarchists would describe them and you might get an idea of what anarchists are actually fighting for.