Without wanting to restart a debate on this, I would like to point out that the opposite argument is true as well. The example could also be interpreted as the "left" wants to force the concept of gay marriage on the "right", that the "left" wants to impose its morality on society and that the "left" wants to change the laws to enforce and codify their point of view.

As with anything else, interpretation of the topic is specific to and the point of view / perspective of the interpreter. The concepts of "left", "right", "liberal", "conservative" are all a matter of judgement and are relative to that interpreter's position at the time. There are no absolutes.

Note: This is not a comment on my personal opinion about gay marriage.