There is no reason given in any of the films for why Dark Side Users wield red blades (or indeed why any lightsaber is a particular colour), but supplementary canon does offer a couple of reasons. From the (Disney) Canon Wookieepedia page we have:
Kyber crystals were inherently attuned to the light side of the Force, and resisted any effort by dark-side practitioners to use them in lightsabers, with one crystal in particular (the green crystal within Jedi Master Kirak Infil'a's lightsaber) subjecting Darth Vader to intense visions that almost drove him insane.18 (Darth Vader: Dark Lord of the Sith 5 comicbook) To this end, a Sith or other dark-sider could use a kyber crystal only by using the Force to dominate the crystal, bending it to their will. This process caused the crystal to "bleed," as if it were a living organism, resulting in the distinctive red or crimson-bladed lightsabers synonymous with the Sith. It was possible to "heal" a corrupted kyber crystal. One known
instance of purifying a corrupted kyber crystal was when Ahsoka Tano purified the two crystals she retrieved from the Sixth Brother's lightsaber following his defeat. In this case, the crystals turned white.13 (Ahsoka novel)
And in Legends (pre-Disney canon) we are given the explanation that Darksiders use Synthetic Crystals that have been imbued with the Dark Side during their creation:
Most synthetic crystals were red, a result of the forging process, and often times the initiate's intentional manipulations, as most individuals who utilized synthetic crystals were Darksiders. The red-hued lightsaber blades generated by such crystals were often nicknamed "bloodshine blades". The crystal's ability to change to reflect the intentions of the creator could be said to foster a stronger bond between the resulting lightsaber and the wielder. However, synth-crystals could be made in any color, requiring only
slight adjustments of the creation process and special manipulations through the Force during the forging.
While these answers give conflicting information, as is to be expected of differing creative teams, they share the commonality of making a lightsaber easier to use for a Darksider, and of a link between a crystal (and therefore lightsaber) and the one who uses it, sort of like the bond between a wand and a wizard in Harry Potter, although to a lesser degree.