Kylo Ren's lightsaber crackles because it has a cracked and unstable Kyber crystal that turned out the way it did after he poured his negative energy into it during the bleeding process of the crystal. Due to Kylo Ren's bottled-up emotions and confused state, the bleeding process made the crystal unstable.
The lightsaber's redesign was a byproduct of the bleeding process that damaged its kyber crystal, rendering it dangerously flawed and unstable, and necessitating the lateral vents were meant to prevent the cracked kyber crystal from overloading.
We've known for years now that Kylo Ren's lightsaber crackles and sputters the way it does because the kyber crystal that powers its blade is unstable.
I wholeheartedly agree with most of the other answers. The technical reason behind Kylo Ren's unstable lightsaber and his crossguards is because he cracked his kyber crystal.
Kylo Ren's lightsaber had a cracked kyber crystal, which generated an unstable blade. The excess power was vented out the sides, thus creating a crossguard-like design. The most important and prestigious vessels of the First Order had weapons upgraded with kyber crystals from some secret source in the Unknown Regions.
As explained in the expanded lore, Kylo Ren cracked his kyber crystal while bleeding it–which is the process of creating a red lightsaber from its original color, and is something that can only be done through the Dark Side. This caused his lightsaber to spark and sputter whenever it was activated.
Any kyber crystal could be bled by a Force user, including one's own, for example, if they were a former light side practitioner and kept their lightsaber.
Even though Kylo Ren uses a red lightsaber, harnesses the dark side of the Force, and wears a cape, he is not a Sith. Because of that, he can never hold the title of Darth. Instead, he was just a chaotic mess of the dark side (until he eventually found his way back to the light).
We learned in The Force Awakens: The Visual Dictionary that the now-infamous red lightsaber had a cracked kyber crystal. Thanks to The Rise of Kylo Ren #4, we now know that the broken crystal is a result of the bleeding process.
In The Last Jedi, during Rey and Kylo Ren's confrontation in Snoke's throne room, Luke's original lightsaber was split in half, and as shown later on in the movie, the crystal had been divided too, but in The Rise of Skywalker, which takes place one year after the previous movie, Rey is shown to have rebuilt it.
What is the connection between Kylo Ren and Rey? As Kylo Ren himself says in The Rise of Skywalker, he and Rey are bonded not just by their familial legacies (Ren as the grandson of Darth Vader and Rey as the granddaughter of Emperor Palpatine) but by their unique connection in the Force.
A crystal embodies the Jedi as the heart of the lightsaber, and pure kyber has no color until it's bonded to the Force user. This process likely resulted in Rey Skywalker's lightsaber being yellow.
Masters. For other uses, see Finn (disambiguation). Finn, formerly designated FN-2187 ("Eight-Seven"), was a Force-sensitive human male stormtrooper who served the First Order until his desertion and subsequent defection to the Resistance during the First Order-Resistance War.
Gathering his strength, Kylo hurled his Sith lightsaber into the sea. Ben Solo had returned. Ben returned to Exegol, where Rey had confronted Palpatine. She gave him the Skywalker lightsaber, which he used to strike down the Knights of Ren.
Darth is the name given to a Sith. Kylo was his nickname as a boy, Ren was the name of the group whose leader he defeated. Also, he is not a Sith. Not a true Sith.
According to Pablo Hidalgo, of the Lucasfilm Story Group, kyber crystals only bleed during the construction of a lightsaber. So Darth Vader can use Anakin's lightsaber and it will stay blue, and in turn, if Luke or Obi-Wan use Darth Vader's lightsaber it will stay red.
Relatively recently, Star Wars canon established that the reason a red lightsaber is red is because the crystal bleeds after the user does something really, really bad. Meaning, your lightsaber can change colors, and Rey's has changed colors because she's done something bad enough to cause the crystal to bleed.
Black is the rarest lightsaber color in the world of Star Wars. For a while, the only known black lightsaber was the Darksaber, forged a thousand years ago and owned by a Mandalorian Jedi.
It appears rarely in the Star Wars universe—so rarely, in fact, that the current canon recognizes only one carrier of a white lightsaber. Ahsoka Tano, the former Jedi Padawan who aided in the rebellion against the Galactic Empire, is acknowledged as the sole possessor of the white lightsaber.
1 Darth Sidious
As well as being a gifted bladesman Sidious' connection to the Dark Side is extremely powerful, granting Sidious the ability to conduct force lightning.
Healing Kyber Crystals
While it's possible for the Sith to corrupt Kyber Crystals, it's also possible for the Jedi to restore them. The Chronicles of Brus-bu is one of the ancient Jedi texts that explains how Kyber Crystals can be healed after the Sith completes the bleeding process.
Jackson wanted his character to wield a purple blade on-screen. Jackson felt that a unique lightsaber color would enable his character to stand out among the sea of sabers on the screen during the chaotic Battle of Geonosis (from Episode II).