Actually this is not the case and is a common example of where the plot falls apart between cannon and filler.
This is a long answer and took a lot of editing, but try to stay with me and feel free to comment if anything doesn't make sense. First, I will explain why your question doesn't have an answer, then I will explain why.
The reason why the queen killed Ciel's parents
This is unknown because it is never truly revealed in the anime. In the battle it is alluded to that the queen perceived Phantomhive household as a threat to the throne and had them exterminated. As to why they became such a threat is left unclear.
Why is this unanswerable?
The contract that Ciel has with Sebastian pertains specifically until Ciel satisfies his revenge. So once that enemy is listed and the conflict is resolved, the plot would end theoretically. As you probably already know, the manga for this series is still being written by
Yana Toboso so naturally the main villain has yet to be revealed and we are still learning the history of Vincent's past bit by bit as Ciel goes through his adventures in service to the crown.
The concept of the queen being the killer of Ciel's parents was only explored in the anime and IMHO was a fantastic plot twist to keep the anime below 25 episodes and very enjoyable, but...
The black butler anime is only partially canon.
The deaths of Ciel's parents have yet to even be explored in the manga. For this reason (among several other inconsistencies with the manga), the anime has several plot holes. If you watch the first season to completion and then watch Book of Circus or Book of Murder (both of which are canon), then the plot clearly falls apart.
Black Butler II and everything that happened in the latter half of the anime is not canon.
Black Butler contains the following arcs, more details can be read about them here:
- Jack the Ripper (also called the Madame Red arc)
- Houndsworth (anime only, non-canon)
- Shard of Hope (anime only)
- Curry Contest
- Noah's Ark Circus (manga only, adopted later in the Book of Circus OVA)
- Haunted Castle (anime only)
- Book of Doomsday (anime only)
- Conspiracy and Revenge (anime only, death of the queen and end of the anime)
- Phantomhive Manor Murderds (manga only, later adopted in Book Of Murder OVA)
- Luxury Liner (manga only)
- Public School (manga only)
- Emerald Witch (manga only)
- Blue Cult (manga only, and current arc at chapter 117 released June 2016)
- Black Butler II doesn't have a place in the storyline as of yet, but will be added at the end here because it does exist.
So a prime example of this is that if the queen was killed in
Conspiracy and Revenge, why is Ciel still taking a mission from her in
Public School which clearly occurred after?
So to sum all of this up, the manga does not support the fact that the queen killed the parents of Ciel. So if the anime did not fully flesh out why that happened then there is no answer.
PS: I can list the more major plot differences anime-wise and manga-wise, but it will take me time to look up arc names and whatnot so this answer will be getting edited.
PPS: Finally finished all my major edits. Anything else beyond this will be for style and added clarity.