Most fears are, at their root, not logical.
It's literally part of the definition of phobia: an extreme or irrational fear of or aversion to something.
Therefore, there may be no logical reason for the fear, at all.
Religious law
- "Whoever touches a human corpse will be unclean for seven days." ~ Numbers 19:11
- "Anyone who touches a corpse, the body of a man who has died, and does not purify himself, defiles the tabernacle of the LORD; and that person shall be cut off from Israel." ~ Numbers 19:13
- "This is the law that applies when a person dies in a tent: Anyone who enters the tent and anyone who is in it will be unclean for seven days" ~ Numbers 19:14
- "He must not enter a place where there is a dead body." ~ Leviticus 21:11
So perhaps your world has a religious law or series of laws that severely punish those who touch the dead. Or that otherwise limits how one must interact with the dead. "Because {god/the gods} said so" can be an extremely powerful force.
Supernatural reasons/Superstition
You specifically rule out zombies. But does your world have other supernatural things? Ghosts, other undead like vampires, etc.? Or more importantly, do the people of your world think these things exist? The reality doesn't have to match the superstition. See also the vampire craze during 18th century Europe.
Medical reasons
Perhaps contagious diseases are rampant in your world. Or carrion eaters are particularly nasty / carry bad diseases. If this is the case, or was the case for a long enough time, fear will be instilled in the beliefs of your people.
Side note
One side note that isn't really part of the answer to your question. But there's a ramification of your fear-of-the-dead that needs to be discussed.
Without a willingness to study the bodies of the dead, two major branches of science in your world will suffer. Medicine and forensics.
Medicine benefited a great deal from the study of anatomy. This study was greatly improved through the dissection of corpses. The history of that study is rather grisly, but without studying anatomy, the science of medicine would be severely hampered.
Would the concept of an autopsy be possible in this world? Without that, finding a cause of death is impossible. You've completely changed how forensic science and police investigations deal with deaths. Murder or accident? Who knows?
Lastly, if you must burn the body, you've just consigned family members to homelessness every time someone dies in their home. When grampa dies, we must burn his corpse. If he dies in bed, too bad, the house just burned down. (If he dies in a restaurant or store, do they set fire to the body, there, in the restaurant/business/store?) I hope you understand what a major impact that can have on society as a whole. (Unless some people are brave enough to move the body prior to the flames?)