@Escheron its not inherently derogatory, homo is shorthand for homosexual. just as hetero is shorthand for heterosexual, and bi is short for bisexual
why is hetero and bi fine (bi is even the standard) but homo isnt? it really depends on context. and yes, culture plays a role, as in some cultures "gay" only refers to homosexual men, so saying "gay" doesnt include all homosexuals, so they would say homosexual, or homo for short, to refer to both, as its easier and faster than saying "gays and lesbians"
context and intent really does matter