I think it's not all for people to suffer from things they don't realize they're suffering from because of the tendency to assume our own experiences are much like those around us. Many people with debilitating migraines, for example, just don't realize that's not just a normal thing everyone deals with. Likewise, many trans people just assume everyone else is masking, so that's just a normal part of being part of a society. This is doubly true for ND trans people, whom would be taught to wear a mask whether they're trans or not, but not exclusive to. Combine the tendency to normalize our experiences and dissociation to dull the sensations, and it's easy to simply not realize it's there until a light is pointed at it. Additionally, many of us lacked the language to describe our feelings: either totally unaware of option if being trans at a young age or having some transphobic or stereotypical "always known and clearly fit the expectations of their gender" trans image that you don't want to be or don't quite fit.

As for other people, it depends. Some may just accept it. No explanation needed (which is technically always the case imo).

Some may be enthusiastic but skeptical. My brother was in this camp - I've been pretty open about a lot of things with him, so I get why he would be skeptical when I suddenly brought that up. But he clearly wanted to be convinced and just wanted me to talk about myself. It's what I wanted at the time because of my own uncertainty... I sorta wonder if he played the skeptic intentionally, knowing that's what I wanted. In this case, the conversation involved more personal details, so no clue how it would go with someone I'm not comfortable going into details with.

For me, I think the easiest way to organize my thoughts was semi-chronologically, rather than by importance, because making judgements about what seems more or less important seems like effort. Going though and writing out your own thoughts before can probably be helpful. If for no one else, for yourself since you seem to be playing the role of enthusiastic skeptic.

I don't have experience with coming out to transphobic people yet... only testing the waters. But you don't really owe anyone an explanation. Best of luck with these people.