Look, this stuff isn't difficult.
1. Liberals/democrats are right-wingers. Just because you (ie Americans) cut off the entire left side of the spectrum with the Red Scares and then managed to delude yourselves into thinking that liberals are the left and conservatives the right doesn't make it so, liberals are moderate right-wingers and conservatives are hard right-wingers.
2. Antifa has nothing to do with the right, neither with the liberals nor with the conservatives. Antifa is made up of left-wingers (socialists, communists, anarchists, etc) who join forces to oppose fascism. Antifa hence does not have a specific political goal outside of fighting fascism, it's just the result of leftists putting their differences aside to cooperate in fighting fascism.
3. The reason Antifa fights fascism is because the left is the primary target of fascists, the camps in Spain, Italy, Germany, etc filled up with leftists long before the fascists moved on to different targets. In other words, because fascists constitute an existential threat to leftists. The fascists don't care what specific type of leftist someone is, hence why leftists go "We have a common existential threat, let's cooperate to fight it" and Antifa is the result of that.
4. Fascists don't give a flying **** about free speech, it's just a way for them to get the liberals to do their bidding. When fascists come together to march it has nothing to do with free speech, it has to do with asserting power and control over the streets. If they are not countered it feeds into their self-esteem and feeling of power and they'll continue to hunt leftists/minorities/homeless/etc in the city after the march.
5. Fascists are really cry-babies. If they do get countered then after the march they go home to cry about it on the internet and the city remains safe from packs of fascists hunting people. That crying and complaints about free speech are simply a way to get the liberals to do their bidding for them.
6. Violence is the only language they understand and it is also the only language they speak. It's not like everything else hasn't been tried on them already. It simply is what it is, hence the saying "If you can't convince a fascist then acquaint his head with the pavement."
7. Antifa does not defend liberal capitalist democracy from fascists, almost all people in Antifa are leftists and hence anti-capitalist. However the unspoken rule in Antifa is that internal political differences are set aside to fight fascism together, and that outside of that groups or individuals just do their own thing. Meaning that, even though Antifa is leftist in the sense that almost all people involved are various shades of leftists, Antifa itself merely exists to fight fascism, nothing more and nothing less.