One should not call to come out and convince anyone that this is necessary. You should always take into account the individual situation of a particular person.
For example, when I work with teenagers, the first thing I say is: "Ok, you want to make a coming out. What expectations about this do you have inside?" And the teenager says:" I expect my mother to cry, hug me and say, "Finally, there is no gap between us". "Okay, now let's imagine that you are drinking tea with your mom, you are having a trust-based talk, and you tell her that you are a lesbian. What's then? And the child says that the mother begins to beat the dishes, drives her out of the house, shouts: "You're a slut, your grandfather is a priest, how can you?" So, the child is waiting for love and acceptance, but realizes that in reality the events will develop differently. Then look for options. Maybe you shouldn't open at all? Especially, if there is a real threat, and for example, a try to put a teenager in a psychiatric hospital has already been made. You should always consider risks and resources.
At the same time, there are also opposite situations - expectations that are incommensurable with reality. Example: an adult, a fulfilled person, met a beloved man, lives with him, but does not communicate with his parents, because he is afraid to confess to them. He misses them very much, but he says: if they do not accept me, I will die. "Okay," I say, "let's think about how you die. They kicked you out of their house. What's then?" He says: "Well, I guess I'll go to my home" - "Super! How will you die?" And he begins to understand: something is wrong here. Somewhere the error crept. It turns out that he still does not have relations with his parents, he still cannot be close to them and deprived of the opportunity to tell them about his happiness. And if he confesses, then at least there will be a chance.
The stage of risk assessment is in any case very important. If we are talking about teenagers, it is better if someone else will be by a teenager's side at the time of making a decision about coming out to relatives. Not because I do not give children the right to independent choice. They are just too "inside" the situation, and their field of view is very limited by this situation. Maybe you should consult a friend, another trusted person who knows the parents? Listen to what he thinks about the idea of telling mom and dad everything? Just get an alternative point of view, which will allow from the extreme (unjustified expectations) to get a little closer to the "middle", understanding of reality, the most probable scenario.
When the parents find out that their son is a gay, their daughter is a lesbian, or, for example, does not feel that he or she belongs to the sex assigned at birth, they experience the classic stages of grief. The grief of loss of the image of the child, their plans for him (for example, about grandchildren). According to another scheme, it is impossible to live through a coming out. At first there will be always a shock and a stage of denial. Parents often perceive children as their continuation, as a certain part of themselves: "I have created!", and therefore they deeply experience the loss of their illusions.
For some time a person will be beside himself. Either he will fall into a stupor, or he will start to "tear the hair on the head". Some parents begin to blame the child. Some blame themselves: "I am a bad parent, I will go and hang myself." It is important to remember here: all this has nothing to do with you and your sexual orientation, all this bears no relation to you as a person. All this bears relation to the fact that the parent invented to himself an excellent story about how your life will develop, and then suddenly opened his eyes and realized that this story would not happen.
Parents need to be given the opportunity to be with their grief. Ideally – leave alone for some time, do not try to pull out love and acceptance if they did not appear immediately. The shock can turn into a silent desire to bring the life back to the state when nothing was known. In this case, the parents behave as if they know nothing. But usually everyone, one way or another, comes to acceptance. An analogy can be made: in a family where there is not a single red-haired child, a red-haired child is born. I know an example when husband's relatives did not even meet a woman from the maternity hospital as they thought that she "walked the baby". Yes, first was the shock, but how can you not accept a child? Should you be repainting him throughout the life?.. Or, finally, take and read about how people inherit the hair color.
One must, however, remember that acceptance does not always happen. There are people, especially religious ones, who are under no circumstances ready to embed new knowledge into their world views.