My apologies for this not being spotted earlier.
how do you justify your statement that asexual marriages cannot exist?
Laws are based on mores, traditions, case law/ common law, statutes, religious texts. All these play a role, none of them being unimportant.
The most ancient and ubiquitous text in the West is the Bible.
In concert, very many tribal communities maintained a monogamous practice of marriage [not all, but many] Again, not all, but many, animal populations mate for life.
Mating and marriage are related. To suggest otherwise is blatant denial.
Marriage, it can be argued, is to protect women and children. It is a socially enabling institution providing predictable results and community stability and financial predictability.
With all contracts there is valuable consideration. Rights and responsibilities are opposite sides of the same coin. Younger fertile couple are expected to have sex. A man and a woman can and do and should claim it as a right. [note: can, do, and should]
The contract of marriage not so entered into is not a valid marriage.. Paul's writings in the new testament affirm principles given in the Tanach.
There is no, and can never be, an institution called marriage between two men or two women. What may exist now in some jurisdictions is a 'fiction' - and should be tested by a grand jury of 24 adults congnizant of nullification.
If Gay couples want to marry, they should, for convenience, and expedience, marry a member of the opposite sex.
Aside from this; statistical abnormality cannot be statistical normality. That would be lying.