Re: Marriage is an institution that is unnecessary in modern society
Overall your grammar is good.
You have one case in which you separated your subject from the verb with a comma. Delete the comma.
I would question the use of "civilisational."
The "I do not see a point..." sentence requires some attention.
I have never heard of "a regress" or "a progress."
From a "sound argument" perspective, a child had a mother and father (assuming a heterosexual union) regardless of whether the parents are married. Do you think the children of Brad and Angelina wonder who their paretns are? Additionally, partners can be partners for life without being married, and getting married does not mean they are partners for life. These "supporting points" don't support your case. (I will ignore the point about marriage being between a man and a woman.)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.