1. the humanist-human rights approach
all men and women are equal before the law and shouldn't be discriminated against on the basis of sexual orientation, cultural group affiliation or capacities, among others.
marriage (the recognition before the law of a relationship involving consenting adults, regardless of the quantity there being involved and the resulting combination of sexes) is a right, not a privilege. not allowing homosexual marriage is a targeted, genophobic, violation of human rights.
some may still say "why do they HAVE TO get 'married'? why don't homosexuals just get an alternative marriage/ a para-marriage?" to this we answer "why don't we let homosexual couples decide for themselves whether THEY want to get married or not--whether THEY want to get married, para-married, submarried or not married at all?"
2. the political approach
a homosexual is a human being, a citizen, a member of a cultural group (a minority), a tax-payer and a voter.
violating the rights of a minority and countering the best interest of a more equitable and tolerant coming generation that is being artificially silenced (for citizens under the age of 18 are not allowed to vote), just in order to please an accidental, loud and genophobic, majority, is not only an immoral and coward crime against humanity; it is also payed over the medium and long term with retaliation votes from more equitative and solidaire coming generations (think about the way republicans lost the south after the civil rights movement, or maybe not).
the homophobic vote is dying out and it is not reproducing itself in younger generations at a significant rate. the zeitgeist of the new generational curve is more inclusive, more socially responsible, less discriminatory.
step in front of the steady march of liberty, equality, sisterhood and brotherhood at your own peril--you may be remembered as an agent of intolerance, genophobia and discrimination in your community, and your children and grandchildren may develop a german-like affinity for your memory.
3. the religious approach
love is god's party. god is for your love to your homosexual neighbor as well as for the love that he or she professes for his or her beloved. god blesses homosexual love as much as motherly love, fraternal love or heterosexual love, for god doesn't discriminate on any basis and her power and love are infinite, as much as your understanding of her ways is limited.
marriage is the church's party. marriage is a celebration of divine love. your church does not have the authority to deny homosexuals the right to marry within their religion, for your church, or whichever priest, is nobody to judge the intentions of the almighty or to interpret them, but to endorse the cause of love, tolerance, harmony and communion, and to safeguard this love within the sacred fortress of marriage.
4. the socioeconomic approach
homosexual marriage would provide some couples with incentives to live together--it would create the bases for a long-term commitment akin to that of any other existing family to take place. this would have net positive effects on the economy and on the environment, since economies of scale would be exploited (all other things equal, consumption of energy per person would decrease, and more credit would be available at more biheaded households).
economically speaking, there would be better opportunities for children to develop at a government-approved same-sex household vis-à-vis growing up in an orphanage or the streets, which brings us to...
5. the societal approach
some people that oppose gay marriage do so because they believe that if government tested and certified same-sex couples are able to foster children or to adopt them, fostered/adopted children may be exposed to certain risks.
children ARE exposed to greater risks at orphanages, extremely dysfunctional families, or the streets.
besides, there is no reason to believe that the same-sex couples that may have passed the same test as heterosexual couples may end up being more problematic than the rest of the couples.
6. the bioethical approach
some people like to define marriage as the union of a man and a woman because solely this type of union provides offspring. this definition fails to recognize heterosexual couples unable to bare children as men and women--why should they be allowed to marry, when their union doesn't make "biological sense"? plus, a member of a lesbian couple may be willing and able to bear a child, and her same-sex couple would certainly represent an asset at the time of raising her child.
let's move forward from capability-determinism: some heterosexual and homosexual couples may not be able to bear children--science and technology SHOULD fix this problem, along with blindness, deafness, cerebral palsy & co.