Snape is not a coward ,he's so brave though , the word coward make him angrey because he was doing everything Dumbrldore asked him to do and on the other hand he's recieving a coward calls . and he didn't response in a bad way , did he ? he just reacted without hurting Harry .

When Harry tried to cast Unforgivable Curses on Snape and called him a coward, Snape did not hurt Harry for that. He was just really angry. I thought there was something hidding behind his reaction. It seemed he had done something special for Harry (kept Harry alive for example) though he had to kill Dumbledore. Of course he didn't expect Harry calling him coward after he had saved him.

He's neither a drama queen/king or coward. He came from a bad family, with an abusive father and obedient mother. The fear of being a coward could come from his Death Eater days, too.

Snape is neither.

i think that snape is one of the most intersting charactors he had all these horrible things happen in his life starting from when his parents argued when he was a child to when lily broke his heart i think that neither lily or snape was right they both had there resons for there actions and then after lily broke his heart she ran away with snape's enamy and then he accadentally sold lily and jame's son to voldemort which meant and he understood that it meant voldemort would kill lily. then lily died and her son was the one who lived it must have been crushing for him and the son ended up being like james and lily and that realtion to lily i think frusterated him and it made him see only the bad in harry and not the good then in the 6th book dumbledore one of the only people snape cares about that is living tells him that he must kill him amagine it your best friend / hero saying that you must kill them because some stupid little kid was told to kill them. so i think he is sorta a drama queen but he has good reasons and ther is no way that he is a coward it just is one of the charactoristics that do not apply to snape. snape also finally looks at the good in harry when he is dying and says the best and sadest line ever "look at me" and then the green found the black and snape's grip on harry's robes slackend and snape move no more i think that is so said. but snape had such a hard life so he has the right to be a drama queen

Was there another reason maybe he reacted so wildly to that particular insult?

I think Snape may have reacted badly to the "coward" insult for several reasons past and present.
1.As a child it is implied he was a sad child before coming to Hogwarts. He may have had regrets that being so young he responded emotionally (as a child would) to the abuse or neglect at the hands of his parents. He may had wanted to respond physically against his abusers but did not have the strength or skill.
2.As a teen relentless teasing at the hands of James and Sirius may have cast him in a cowardly light to other Hogwarts students.
3.As an adult Sirius and Bellatrix both make comments concerning his absence from the actual "fight". Since we know he is a spy he could not tell them all he had done and personally sacrificed for both the Order or the Death Eaters.

Is Snape a coward, or was there something he did in the past that might be seen as cowardly? If so what do you think it was?
No Snape is not a coward. (Because I love him so much!)I think the Snape's Worst Memory scene may have cast him in a cowardly light, because he was unable to defend himself right away by quite a few students.

Is Snape a coward or was he just lashing out because he was angry at having to kill Dumbledore?
I think that Snape was very hurt and angry at having to kill Dumbledore. The headmaster gave him a chance when no one else would, and sees Snapes heart. Severus knows this and appreciates the fact that at least one person in the world understands him. ( Oh my I sound like a fanfic! )Dumbledore trusteed Snape to do the most dangerous work in the Order. Snape having the personality of an overachiever may have felt honored to take on this challenge for Dumbledore

Snape is a confusing character: he has been a coward by telling Voldemort about the prophecy, he has been a drama queen because he has lashed out at Harry and been an unfair teacher to him due to Harry's dad's acts (which Harry has nothing to do with), andhe has been brave as he has done things for Dumbledore which have saved peole's lives.

I don't think that snape is a coward, he Is just more upfront about his attitude (dont reapply think that that made any sense at all but...

I have no idea what to think.He is a confusing character.