I can't say I've found myself in the middle of an argument yet, but there are ways of going about a conversation that can keep it from getting out of hand (...) in some cases, though, it's just best to walk away.

There are two extremes: at one hand the very heated and aggressive arguments. Tears are shed, ad-hominems are frequently used, sometimes it goes as far as death threats and physical violence. That's like the Internet I grew up with. The other extreme is the echo-chamber effect where people with different points of view simply does not interact with each other, and where those that do interact with each other always agree and support each other - and if someone comes with any criticism, they are moderated away, downvoted or flagged into obscurity. The latter is a growing trend; we're seeking out similar-minded people on the Internet, it's often more comfortable to just walk away if we see something we disagree strongly with, and the social networks are to some degree encouraging this trend. With Steemit, there is even an economical intensive to agree with everyone.

Both those extremes are very bad, ideally we should find some middle ground. Friendly arguments where one exchange viewpoints and arguments in a rational and polite manner is both good and needed, hence I think it's important to reach out and tell when disagreeing with things, rather than to simply ignore it and walk away.