It could be related to his motive for killing people. Since you say "knives and blades" that seems more elaborate than just stabbing someone in the back and suggests that the method might have significance. Say a revenge for a murder committed with blades. Or a cinematic professional killer might have a specific modus operandi or trademark for advertising purposes.
Blades are also more silent than guns. Even if you use subsonic ammunition in a suppressed gun, the bullet is driven by an explosion. It won't be quite as silent as a knife. For someone who hates making noise it might be valuable.
Blades can also make less of a mess. If you stab someone so that he dies from it and leave the blade in the wound, there might be minimal blood splatter. Guns in contrast are difficult to use clean. Even if you succeed in avoiding the blood, you will probably have propellant residue all over yourself.
He might prefer killing close range to avoid mistakes. This would negate much of the edge guns have over blades.
You can build an improvised blade from any suitable size piece of metal, plastic, or wood. They are inferior to real fighting blades for combat, but kill just as well. Building improvised guns is a pretty good way to lose fingers and even then you'll need to carry ammunition. So if you have a killer who does not want to carry weapons around or buy weapons or ammunition from unreliable sources, blades do make some sense.
Another benefit of improvised blades is that you can easily dispose of them. As long as they are not covered in blood near the site of the murder, they might be discarded as trash. Wrap it in paper and put in a trash can and it is probably safe. Guns in comparison are much more expensive to discard and can be recognized as the murder weapon and traced.
They limit your tactical options, but if the killer is a methodical patient type who is willing to wait until he has a safe opening to kill without fighting, blades do still work. That is really the key in my opinion, since using blades instead of guns limits your options, the killer must control the risks some other way. Stealth, disguise, preparation, etc. The methodical, patient, and precise personality.