The arguments against are usually religiously based or 'traditions' based (it's never been done, it isn't how it has been done, why should we do it now is the 'tradition' type argument).
Those favoring same-sex marriage make a very important distinction. Civil marriage versus Religious marriage. With the traditions argument it almost always comes down to the imagery of a man and woman walking down the aisle of a church with a reverend, etc at the front...the bride in white and the men in tuxedos. That's the tradition (never mind that other religious groups' religious marriage ceremonies are completely different). Thus for the 'traditions' argument, it is based upon 'religious' marriage and most of the tradition arguments start going into religious arguments.
The point being distinctive here is that there is, actually, two forms of marriage.
Civil marriage : a legal binding contract instituted and regulated by government that contains certain benefits as well as certain restrictions to those that choose to enter into this contract.
Religious marriage : a spiritual union done in the eyes of the divine for blessings, etc. it also is a contract between the couple entering into the arrangement and their religious institution. the religious institution then provides certain benefits and restrictions within its sphere of influence.
What the people arguing for same-sex marriage are talking about is civil marriage. Advocates of same-sex marriage in now way want to infringe upon the rights of religious institutions to regulate and maintain their religious marriage regulations, rules, etc. However, because homosexuals pay taxes, not to a religious institution but to the government, and these taxes are often what is used to help provide the benefits of marriage, and that the civil marriage also holds government/civil protections...same-sex marriage advocates are asking for civil marriage...the marriage regulated by government.
You have to pay close attention to the arguments, because both are equally valid. Certainly the government has no right to impose upon any religious institution the requirement of performing a marriage it does not condone....but the government does not regulate religious marriage...it only regulates civil marriage. And people aren't necessarily talking about changing the 'tradition' of marriage, they simply want to include more people into the civil marriage aspect. The traditions of the ceremony and the deeper meanings are regulated by religious institutions. And if we are arguing that for religious reasons same-sex marriage must be denied...then are we not violated the rights of the religious institutions that allow same-sex marriage? Again, though, the distinction being made is that what is being asked of the government is CIVIL MARRIAGE and not religious marriage. Many of the religious institutions that allow same-sex marriages already provide their members with religious marriage....the argument is about the government and whether or not people who are part of this nation and pay their taxes, that all couples...all unions between two consenting adults...be accepted in civil marriage laws.
Again, the argument is not to force religious groups to recognize anything or to do anything that violates their religion...it merely requests that the government not favor any religion and recognize all of its citizens.