The post offended them
If your post offended a person, by going against their beliefs for example, then they might leave a negative comment in response to the post.
They are jealous
Jealous people usually wait for the chance to make the ones they are jealous of look bad in front of others. If a person is jealous of you then they might leave a negative comment for no apparent reason.
They are haters
Haters usually feel frustrated as a result of their hatred. In order to release some of their frustration, those haters might make negative comments on the posts of the people they hate.
They are attention seekers
Attention seekers might leave odd or negative comments in order to attract the attention of other, usually the ones who will see the post. (See Why are some people are attention seekers?)
He is hurt
If you hurt a person, by rejecting them for example, then they might post negative comments on your status just to feel better.
They are anti-social
An anti-social person will usually have a generalized hatred against most people and as a result might get engaged in different behaviors to make others feel good.
They have self-esteem issues
Many people criticize others or make fun of them in order to feel better about themselves. People who have self-esteem problems usually do so.
To pay back
Some people post negative comments on the posts of others in order to pay back for something that happened earlier. Even if you didn’t hurt those people they can believe you intended to hurt them as a result of incorrect perception of events.
They are unable to handle conflict
Some people have low tolerance for accepting differences. In such a case, your different beliefs can annoy those people and motivate them to respond in a negative way.
They are bullies
A bully will usually try to find a victim to exert his power on him in order to feel better about himself.
They are in a bad mood
When a person is in a bad mood he might project his anger upon others. In such a case, the person can experience a little bit of a relief by attacking the ones who never harmed him. (See Why Am I in Such a Bad Mood?)
To look different
Some people post negative comments in order to stand out from the crowd. Those people might not have any bad intentions as their goal might just be to stand out.
Why some people leave negative comments on your social network posts?
Why do some people post highly negative comments about other people on social media?