In the name of equality the government plans to require gay marriage and heterosexual marriage to be recognised as the same legal institution. But if this is equality we should call it "people's equality" to make plain that it's about as authentic as "people's democracy" was in East Germany.
Superficially, the government's reasoning appears to have some connection with the universally accepted belief that everyone should be equal under the law. But this assumption fails to acknowledge the two main forms that modern law takes. Many laws prohibit specific kinds of behaviour on pain of punishment, and it is fundamental to a free society that all such laws should apply equally to everyone.
However, not all law is of this kind. Some laws do not prohibit (or require) behaviour; rather, they create facilities for human co-operation. For example, we have company law for commerce and it is possible to register as a PLC, a non-profit company limited by guarantee, a co-op, or a community interest company. By creating legal vehicles for people to work together as they believe best, the law simply recognises the diverse ways people have chosen to trade with each other. Individuals are free to choose their preferred style of conducting business and to adopt the legal vehicle that suits them best.
Current marriage law also involves legal recognition of a chosen type of relationship. It does not exclude anyone from adopting another approach, any more than registering as a PLC excludes people who wish to trade as a co-op or provide a service as a charity. When gay activists complain that heterosexual couples have a separate legal institution it is logically similar to a PLC executive complaining that it is unfair discrimination for a co-op to have a different legal structure.