The essence of leftist reasoning is emotion, not factual critical thinking. These are emotional creatures that are forever concerned with their social standing, which is tied to their sense of worth. A lot of it boils down to prioritization of what other people think of them. If you try to argue with them like you would us, you'll forever be missing the target if your goal is to convince them of anything. You must learn to grasp the underlying emotions that dictate their thinking and address that before you can ever hope to reach them with any kind of logic that we use.
I've learned that the key is never to take what they say at face value, because they don't mean what they're actually saying. No matter what comes out of their mouth, you have to ask, "What feeling makes them say this?" Otherwise you'll never understand them. You also have to ask, "What will they feel when I say this?", before you speak. It's kind of like navigating a mine field. One wrong step and you'll detonate a hidden charge of cognitive dissonance. It'll blow off your leg and you'll have no leg to stand on as far as they're concerned. Fortunately these people also tend to have terrible memory, so you can usually start again after some time has passed and they forget.
Have you ever heard someone say, "liberalism is a mental illness?" To reason with a leftist, start by realizing that this is fundamentally true. (As much as I hate equating the term liberalism with leftism.) You need to stop thinking of these people as fully functioning human beings and start thinking like a psychologist. These people are not well. They need help, they're sick. I don't mean that facetiously. These are people who have been mentally, and sometimes physically abused as children. It's caused long term damage to their psyche and they obviously haven't worked through these problems.
I shouldn't need to explain how longterm, toxic stress and abuse during critical developmental stages of the brain can lead to stunted cognitive growth. In fact, there's been a great many situations I've encountered where people have literally become emotionally trapped at what appears to be somewhere around age 10. When they encounter more stress than they can cope with, they fully revert back to this and behave exactly as a child around that age would, which may in fact be what you're running into by the way. Some of the people I'm thinking of have been in their 30s… 40s… 60s… This doesn't go away on its own. For example, the ex-wife of someone I know would exhibit amnesia and begin speaking fluent French which she learned as a child, but completely lost all memory of as an adult.
That's just one example though. The mental illnesses involved can be many. There could be some sort of manic depression or other emotional disorder involved. Think about it, how do we view Tumblr?
Mentally unstable attention whores that love to fake suicide attempts, right? encyclopediadramatica.rs/Tumblr
Delicate snowflakes? encyclopediadramatica.rs/Special_snowflakes
LGBTQRSTUVWXYZ++ individuals who glorify the act of self-mutilation? encyclopediadramatica.rs/Transgender
Teenagers with what basically, and often literally, amounts to a fetish for cutting themselves and putting it on display? encyclopediadramatica.rs/Cutting
Cloppers? encyclopediadramatica.rs/Bronies
Furfags? encyclopediadramatica.rs/Furries
Attention-seeking white knight SJWs, who I've concluded often are the type to actually rape women when the opportunity presents itself?
Last thing I want to point out is that because these individuals are so focused on emotion, they're also very quick to pick up on yours. The old addage, "sometimes it's not what you say, but how you say it", is especially true with these people. For best results, remain patient and approach with a white mentality… That is, approach them with the desire to care for them. One of the virtues of the white race is our great capacity for compassion. We are an instinctively empathetic race. The Jews may have exploited our sense of compassion to manipulate us, but it remains a virtue nonetheless when coupled with knowledge. Compassion is no weakness. Don't lose sight of the fact that our pride isn't about hatred of other races, but about love of ours. Embrace the dignity of your heritage… Or even if you're not white, perhaps you can still aspire to emulate our virtues. I would respect that.
Take breaks as necessary so that you can remain calm. As one of the other anons mentioned… The goal of their method of argumentation is generally to frustrate or upset you. Binary thinking: Us VS Them. Their goal is to win a fight. Your goal should be to heal them. Don't fall into the trap of doing the same thing they're doing.