One group of people seek to withold a right/privilege/activity from another group, whereas the other group seeks to make the right/privilege/activity avalible to all. You can not suggest that each group are equally trying to force their beliefs on the other.
After much consideration, I've decided to refer to my "dog" a "camel". In fact I demand that all of society refer to my dog as a camel. Camels have four legs and dogs have four legs therefore I reject the traditional definition of a "dog" and suggest that anyone not adhering to my demand is trying to force their beliefs on me.
Seeing as changing the definition doesn't appear to me to have any affect on traditional dog owners in society I see no reason as to why everyone won't aquiesce to my demands on this animal rights issue. If society doesn't tow my line then I shall resort to name calling in an attempt to force traditional dog owning society to bend to my demands lest they be considered biggots.
After all, there must be some other country in the world that refers to dogs as camels. I shall raise this country as a golden standard of "camel" (formerly "dog") ownership, even though dog owners in this country were previously able to think for themselves. Of course we could have a public vote on this contentious issue but I fear that society may reject my new dog-camel definition so I'll accuse the whole of society of being camel hating biggots in order to force an act of parliament.