Are there any reasons why Light killed the FBI agent? This is a question that comes to my mind every time I watch Death Note or talks to someone else about Death Note and it is bothering me.

In the beginning, Light went out of his way to kill that one FBI agent on the bus and therefore caused L to suspect him and started the whole sequence of events of eventually discovering the existence of the death note. If Light hadn't killed that FBI agent and just kept writing names down in the notebook in his room, nothing would have happened. 

Was the killing of the FBI agent something that the creator put in just to progress the story or is there an actual legit reason why Light had to do this?

Please, guys, don't give a theoretical answer like "It was because of Light's personality" or "Light wanted to tell the world to not follow L" or something like that, if it is because of this then the creator just did it to advance the plot.
It was a move to try and destroy the entire investigation against him as well as prevent crucial facts from being reported.

At this point, L had used some tactics to determine a few things about Kira.  Among them that Kira lived in a certain region of Japan and that he had access to police information.  Given that, the list of suspects was short.  And given how L deduced that Kira was probably a student, given the timings of killings, etc. that list was only going to get shorter.  Light needed to eliminate L and the investigation as soon as possible so he could kill freely.

Light, through Ryuk, found out that someone was following him and investigating him.  But he was unaware who it was.  He then concocted the bus scheme to force his follower to reveal his identity, learning that he was an FBI agent.

Now knowing that the FBI agents were in Japan, Light followed a similar path in logic to what L took, that they must be investigating those close to the Japanese police.  He also correctly assumed that the police did not know about the FBI's investigation.  He then determined that if the Japanese police became aware of the FBI and thus L's investigation into them, it would cause distrust between L and the police.  This would then hopefully remove any local help L would get.  In addition, it could also scare off anyone else from the international community from interfering with Kira.  At any rate, reducing the number of people Light had to contend with increased his chances of coming out of all this alive.

Also, Light knew he would be under greater suspicion after the FBI agent revealed himself.  Those FBI agents were never supposed to reveal themselves as FBI agents at all.  It would be somewhat suspicious, especially to L, that one was forced to do so.  As such, if L were to find out that the FBI agent had to reveal himself to Light who was already a suspect, it would further increase the suspicion of Light as Kira.  Light knew this and thus needed to kill the FBI agent prior to that information being reported.

So by killing the FBI agent Light accomplished a few things.  One he put the police at odds with L.  Second he reduced the number of people investigating.  And third he was able to prevent critical information from getting reported.