The 'Goths' name was Sophie Lancaster- there is now a foundation set up in her name encouraging tolerance of all groups of people, and a stage named after her at the Bloodstock Festival. She and her boyfriend were attacked for being , as you say, Goths.
Why? Honestly I've no idea except that historically people always attack groups which are dis-similar to themselves, and they usually do so in gangs. This might be because in a gang you have group culpability, group affirmation and group concensus, and gangs appeal to weaker people who are less inclined to stand up and be counted on their own. If you then take a group of people who are all personally insecure and thus prone to displays of egotism when in a like minded group you get scenarios where that group will go far further as a group than any single individual would ever go. Add to that oneupmanship ( drinking more than anyone else, taking more drugs than anyone else, being 'harder' than anyone else) and you have a recipe for disaster, and since none of these people are genuine 'warrior' types they tend to pick on people they perceive as easy targets like a young couple walking through a park who are dressed differently in Sophie's case, gay men because they are (wrongly) perceived as being effeminate, gay women ( because not wanting or needing a man is threatening to them as they are already psychologically de- emasculated), old people because they represent previous authority ( which they are likely to have had a problem with), black people, Muslims, Jews etc simply because they are different and thus scary etc etc etc.
It doesn't excuse it, but it does explain why it's so important to make sure that small children feel valued and respected at school from the word go, their self esteem is nurtured by teachers and parents and they find themselves valued by society and part of a larger and gainful group with good values, because sad, miserable underachieving little kids end up in gangs and gangs do crazy and bad things. (Just for the record I'm not talking about well organised street gangs where drug dealing and professional crime is the purpose), I'm talking about gangs of 'like minded', violent, angry louts with no meaningful place in society.