(although a source on most transgendered people not having gender dysphoria would be appreciated because I think most do. Could be wrong though)

I think this certainly used to be the case, but it has changed in the last 5-10 years. Are you familiar with the "tucute" and "transmedicalist" (aka "truscum") trans communities? The former, and much larger, community, "tucutes," believes that you don't have to have gender dysphoria to be transgender, and attack those who say that being transgender is directly tied to a medical issue. The is the majorly popular view on Reddit, Tumblr, and many other forms of social media, and those who believe in the "transmedicalist" stance are often villified for being "exclusionists".

Here are some of the reasons I've heard for why people identify as transgender, both on the internet and from people I know in real life:

• Feelings of gender dysphoria that lead the person to believe that they are a member of the opposite sex "in their soul" or that they have "the brain of the opposite sex" (even though the claim that a transgender person's brain matches that of the opposite sex, has been debunked by research).

• Moral beliefs. Some people identify as "nonbinary" (a subgroup of transgender) because of their political beliefs; they believe that the best way to reject bigoted sex stereotypes is to deny the idea that they may be categorized at all.

• Gender-nonconformity without any gender dysphoria. When an individual has many behaviors that are go against bigoted sex stereotypes in society (e.g. being a woman who is into mathematics, when sex stereotypes suggest that women are "bad at math"), the people around them may repeatedly question whether they are "transgender and in denial about it" or whether they are "nonbinary". For example, I know a "cisgender" gay man who has had multiple people suggest to him that he ought to "identify as transgender" because he is interested in some hobbies that are stereotyped as being "feminine" or "for women".

• Fetishism. Specifically, sexual arousal to cross-dressing and fantasizing about oneself as the opposite sex. For example, some autogynephilic men who do not have gender dysphoria but do have sexual arousal at the idea of being a woman, choose to transition and they identify as transgender. You can see examples of this on the r/askAGP subreddit on Reddit.

• Peer pressure. It has become popular among adolescents to "identify" as LGBTQ+, and being straight or not LGBTQ+ is deemed boring, negative, or even immoral.

I am probably forgetting some other reasons why people choose to identify as transgender.

It is also a choice to describe yourself as lesbian, bisexual, or gay. Not to be same-sex attracted (likewise with feeling gender dysphoria) but to describe yourself as gay and be in same-sex relationships (likewise with describing yourself as transgender). Thus if one views transgenderism as a choice, then I feel by the same logic they must view being LGB a choice - and this is a dangerous train of thought.

Let's break apart each phenomenon here.

LGB:

• Definition: Someone who is lesbian/gay/bisexual is attracted to humans of their own sex (in the case of bisexuals, they are attracted to both sexes). All L/G/B people experience same-sex attraction (to at least some degree).

• Observation: One does not choose whether or not to experience same-sex-attraction.

• Observation: One can choose whether to acknowledge one's same-sex attraction, i.e. to "describe yourself as lesbian, bisexual, or gay."

• Conclusion: Since (A) same-sex attraction is not a choice and (B) having same-sex attraction is the sole condition for being LGB, then (C) being LGB inherits the "is not a choice" property that the phenomenon of same-sex attraction has.

The same set of logical steps cannot be followed for the T.

T:

The definition of "transgender" and "gender identity" vary widely depending on who you ask. I will use the American Psychological Association (APA)'s definition, for simplicity's sake:

Transgender: An umbrella term encompassing those whose gender identities or gender roles differ from those typically associated with the sex they were assigned at birth.

• Observation: Notice that this definition says nothing about gender dysphoria: you do not have to have gender dysphoria to identify as transgender.

• Observation: People do not choose to feel gender dysphoria (just as people do not choose to feel same-sex attraction).

• Observation: One can choose to identify as "transgender" even if you do not have gender dysphoria.

• Observation (extra): some "cisgender"-identified people have gender dysphoria, and choose not to identify as transgender.

• Conclusion: Since (A) feeling gender dysphoria is not a choice and (B) it is not necessary to have gender dysphoria to describe yourself as transgender and (C) some people with gender dysphoria do not choose to describe themselves as transgender, (D) being transgender does not inherit the "is not a choice" property that the phenomenon of gender dysphoria has.

"Gender dysphoria" != "transgender" to most people. (The less-popular "transmedicalist" view requires that all transgender people have gender dysphoria, but its own separate set of flaws.)

edit: As far as I am aware there have not been any research surveys on the prevalence of gender dysphoria among transgender people; however, there are many specific examples of people who do and do not have gender dysphoria.

Transgenderequality.org's position:

Not all transgender people have gender dysphoria. On its own, being transgender is not considered a medical condition. Many transgender people do not experience serious anxiety or stress associated with the difference between their gender identity and their gender of birth, and so may not have gender dysphoria.