Easy, I would say because It can bring huge financial and emotional stress.
Homosexuals can sue people who are exercising their religious beliefs. For example, a heterosexual married couple with children who do not want to rent a room in their their own family household to homosexuals could be sued for discrimination based on "sexual orientation." This can incur significant financial and emotional stress upon the family, not to mention the "prior restraint" effect of the fear of being sued which results in a family not renting out a room.
Gay Marriage means having the morals of the minority forced upon the majority.
This can also be said in the reverse. Either way, there is a problem. Normally, morals should not be forced on anyone, though there are exceptions. We force morals on others by preventing them from stealing, raping, murdering, etc. So, it is not automatically wrong to force morals on someone. But the issue then becomes what is morally right and wrong in the first place, and altering morals in a society definitely causes stress.
The percentage of homosexuals in society is less than 5%, yet it is being forced upon the other 95% of society in movies, TV, literature, and political periods.