Let's Talk about the Bind
Two fighters size each other up. They strike and parry, back and forth, then their swords lock together dramatically as they hurl snappy one-liners at each other. They shove and circle around, and split apart again, and the fight continues! Except... nah. This is the Hollywood parry, something you'll see in all the Star Wars movies at least. Like many things in Hollywood, it's not a bad thing because it's unrealistic (though it is that) but because it's boring and stupidly overused.
Okay, lightsabers get an almost-pass here because we've never seen them slide - so as far as I know, they don't. They just bind and stick together. (I don't know who thought sticky swords was a good idea, but okay, let's run with it.) Star Wars goes hog-wild with this particular trope as a result, and you do get to see some of the most egregious examples in the prequels.
In actual fencing, with any weapon I know of, this stuff just doesn't happen. Why? Because, as I'm so fond of saying, swords behave like big steel levers, and their lever quality is what wins fights, not sharpness.
Let's take a longsword. Let's say you strike and your opponent parries. One of you, assuming you both actually know how to use a sword and are NOT just flailing around like a baseball player, will win the crossing and catch the other's flat on their edge, and the caught sword will slide down to the crossguard unless the fighter disengages and counter attacks.
What the losing fighter will NOT do is step in and start shoving with the sword. There is literally no point to doing this. What we're taught is that this is misura strettissima, the closest measure, and getting into a shoving match is wasting a good opportunity to grapple your opponent. There are so many other things you could do - grab their sword and pommel-strike them. Trap their sword and throw them. Grab their arm, twist the sword out of their grip, and slap them silly with it.
Half-swording, guys. It's for life, not just for Christmas.
Even for weapons that ostensibly don't involve these shenanigans, shoving with the sword is simply dumb if only because this kind of bind means your sword is pointed at the sky, and not at your opponent.
What if it's edge on edge?
Okay, look. I've already talked about the properties of the sword, i.e. the whole hardness vs. flexibility thing. Swords take edge damage every time they're used, as we all know, as they have to be able to yield a little bit to avoid shattering on impact. To bind, stick, and start shoving, you need some pretty silly conditions to be fulfilled.
Both opponents must be roughly equal strength. (Otherwise one will overpower the other and there will be no bind.)
They have to strike at the same time. (If one strikes and the other parries, the swords will slide and not bind.)
Their swords have to have roughly the same metallurgic properties at the point of impact, such that both get a notch in them. (If one sword is better than the other, it will not get a notch and the swords will slide and not bind.)
The notch must be big enough to hold the swords in place against friction and the strength of two people. (If they're not big enough, the swords will slide and not bind.)
The swords must somehow not bounce off each other. (A bounce, which happens a lot, means no bind is possible at that moment.)
The swords must remain stuck together in spite of two people's shifting weights and attempts to gain the upper hand.
I will say this much - I've never seen this kind of bind in a year of fighting with a longsword, and it's sometimes mentioned as being this silly Hollywood thing in the salle.
And how! Hollywood loves it because it gives actors a chance to toss out a few lines or some strained looks in the middle of the action. But it's just boring, at this point. It's a huge, lurking cliche that won't go away and is almost never, ever done well. It's there because actors want to make sure that people can see their faces, and how good they are at acting.
It also means that other opportunities for characterization are lost, and fight scenes become predictable and tired. Once again, I have to go back to Inigo Montoya versus the Man in Black for an example of the bind done well - they spend the fight tossing quips at each other anyway, but then Montoya catches the Man in Black on the edge of the Cliffs of Insanity and binds him - not sword to sword, but body to body - while he tries to shove him off into the sea. The tone changes subtly, and you can hear the struggle in the Man in Black's voice as he delivers the line "There is something I ought to tell you..." in the middle of the bind, and then - hah HAH! Reversal! "I'm not left-handed either!"
That's the way it should be, not this 'let's hold our swords together and grimace at each other for a second'.
There are almost too many terrible examples to point out in comparison, but I have to give it to Star Wars: Revenge of the Sith. That fight between Anakin Skywalker and Obi-Wan Kenobi. That WHOLE FIGHT is a testament to the fact that money can't buy good directing or writing. A complete clusterfuck is about the most apt description I can give it, and the binds are just one element of inane silliness in a mountain of inane silliness.
Hey filmmakers, would it be possible for you to quit this shit, hire a fight director, and do something better? Pretty please?