I haven't seen any of these arguments actually spelled out succinctly, but this is a list of what most of them seem to be getting at.
- Homosexuality upsets the social order, disrupting the traditional lines of authority and leading towards chaos (moral and otherwise)
- Homosexuality spreads AIDS, harming heterosexuals as well as homosexuals
Homosexuality is condemned by God(see also homosexuality and religion)
- Gay (or lesbian) couples deprive children of a mother (or father), when it has been shown that children do best when raised by a married mother and father. 
- Inquiry: Do any of those studies contrast married-mother-father families with anything other than single-parent families, much less gay couples?
- Homosexuals must make a conscious decision and expend considerable additional effort in order to reproduce, thus minimizing the number of unwanted children for which they are responsible (and hence reducing homosexuals' overall burden to society)
- Many cultural/religious sentiments against homosexuality probably arose in pre-industrial society where maximization of reproduction was vital to survival; we now have the opposite problem, or (at best) no need to maximize reproduction
- Actively suppressing homosexuality causes a great deal of personal suffering and hardship, and puts at least one significant roadblock in the way of homosexuals' "pursuit of happiness", a right guaranteed by the US Constitution
- Failure to legally support the rights of homosexuals as equal citizens allows them to be harmed and persecuted without cause, and gives apparent sanction to religiously-based hatred and violence towards homosexuals
- Failure to grant homosexual couples similar protections and freedoms to those granted to heterosexual couples causes hardship on homosexual-parented families, and harms the well-being of any children they may be raising
Nature vs. Nurture
Much argument about homosexuality centers around the theory (for which there is apparently strong evidence) that homosexuality is an innate biological property, fixed either prenatally or during the first few years of life. This argument is largely irrelevant, for the following reasons:
- Any argument based on the presumption that homosexuality is or is not natural is utilizing the appeal to nature fallacy.
- Defending homosexuality on the basis that it is natural contradicts the stand that homosexuality is not a disease to be cured, the latter appearing to be majority opinion among advocates of homosexual rights.
The argument that homosexuality is "unnatural", as untrue as it may be and as easy as it is to counter, distracts attention away from the true issue of how support for homosexuality would actually affect society.