Here is the relevant part of the text from the link, with my comments:
What does it mean to be transgender?
Transgender people are people whose gender identity is different from the gender they were thought to be at birth. “Trans” is often used as shorthand for transgender.
Babies are not 'thought to be' a gender at birth. They have a sex. It is confusing and misleading to conflate sex and gender
When we're born, a doctor usually says that we're male or female based on what our bodies look like.
Agreed, unless it is unclear and further tests are needed.
Most people who were labeled male at birth turn out to actually identify as men, and most people who were labeled female at birth grow up to be women.
Note the sleight of hand: males 'identify as' men, but females 'grow up to be' women. Identifying is a totally different thing to being. Male babies grow up to be men and female babies grow up to be women, regardless of how they may 'identify' when adult.
But some people's gender identity – their innate knowledge of who they are – is different from what was initially expected when they were born.
The 'innate knowledge of who they are' is a delusion if you are talking about sex. You are either of the male sex or of the female sex. You cannot have 'knowledge' that is just plain wrong, because that is not knowledge.
I guess you can have 'innate knowledge' of your gender, to the same extent and in a similar way that you can have 'innate knowledge' of your immortal soul.
A transgender woman lives as a woman today, but was thought to be male when she was born. A transgender man lives as a man today, but was thought to be female when he was born.
The words 'lives as' are never fully explained. How does a male person 'live as' a woman if they are a man? He can change his documents and his name. He can dress in a stereotypically feminine manner. He can adopt 'feminine' mannerism and interests. He can sneak into the female toilets. He can ask everyone around him to use female pronouns about him.
None of this is 'living as a woman'. It is pretending to be a woman.
Some transgender people identify as neither male nor female, or as a combination of male and female. There are a variety of terms that people who aren't entirely male or entirely female use to describe their gender identity, like non-binary or genderqueer.
We a dimorphic species. Everyone is either male or female.
(Note: NCTE uses both the adjectives “male” and “female” and the nouns “man” and “woman” to refer to a person’s gender identity.)
Well that is a recipe for confusion and obfuscation! If you cannot talk about sex and gender as two different things, how can you explain anything clearly.
Everyone—transgender or not—has a gender identity.
No. There is no evidence to support this assertion. Many people claim they do NOT have any gender identity. If you want to assert this, you have to first of all precisely define and explain what a gender identity actually is, then go about proving that everyone has one.
How does someone know that they are transgender?
People can realize that they're transgender at any age. Some people can trace their awareness back to their earlier memories – they just knew.
Memory is a fascinating and slippery thing. It is very clear that people can be mistaken about facts and events they remember from their childhood, let alone how they felt about themselves.
Others may need more time to realize that they are transgender.
Some people may spend years feeling like they don't fit in without really understanding why,
Typical of undiagnosed autism.
or may try to avoid thinking or talking about their gender out of fear, shame, or confusion. Trying to repress or change one’s gender identity doesn’t work; in fact, it can be very painful and damaging to one’s emotional and mental health. As transgender people become more visible in the media and in community life across the country, more transgender people are able to name and understand their own experiences and may feel safer and more comfortable sharing it with others.
For many transgender people, recognizing who they are and deciding to start gender transition can take a lot of reflection. Transgender people risk social stigma, discrimination, and harassment when they tell other people who they really are.
Nobody should be subject to discrimination and harassment. There are laws against it. Gender Reassignment is a protected characteristic.
Parents, friends, coworkers, classmates, and neighbors may be accepting—but they also might not be, and many transgender people fear that they will not be accepted by their loved ones and others in their life. Despite those risks, being open about one’s gender identity, and living a life that feels truly authentic, can be a life-affirming and even life-saving decision.
That last bit, hinting at suicide, is totally irresponsible emotional blackmail. It implies that if you don't let a transperson 'live a life that feels truly authentic', they may end their own life.