As we know, taking something from an animal for mass human consumption will usually end in the death of animals, as in in the egg industry male chicks are killed for example. Is it right to go straight to this as an answer when a non veg*n asks 'why dont you eat (honey/eggs/something that is seen as not directly harming an animal)
I sometimes feel that talking about the deaths of animals, although factual, can come across as "guilting" change in people that dont want to, and may even result in them disconnecting further with the cruelty.
I don't think there's a right thing to do, it depends what you're after.
But if you want to avoid people being offended, I've always mentioned this and never had a problem with people thinking I'm guilt tripping them. I think there are two main things that I find stop people being offended are:
1. Only bring it up, if asked (or if the topic of conversation has already been bought up). The main thing that seems to irritate people, is bringing up animal cruelty when people aren't interested (and I've seen it done, and I've seen them be called preachy later, which seemed to reinforce my point to me).
2. Don't try to convince anybody. Just state what you believe, explain it's what you believe. Don't hold back on what people are asking you for, but don't turn it into a debate either.
I'm not saying don't be honest, because I'm happy to say "I believe the dairy industry is wrong because it kills the calves required to produce milk" or when asked "I don't believe people should consume dairy, if it was down to me, nobody would", but I avoid convincing people and I avoiding bringing the topic up myself and I have never had anybody call me preachy or be offended.
Anyway that isn't general advice... it's just my experience, if you want to avoid offending people. If you don't mind offending people, and want to change peoples minds and choices, this advice isn't for you!