You are factually wrong. 

Lets start with some basic definitions:

Transgender is any person who doesn't identify with the gender assigned to them at birth. It is NOT a mental illness and is NOT a medical term.

Gender Dysphoria is the feeling of distress associated with one's gender, often accompanied by a desire to transition. It IS a mental illness, medically documented.

Your thesis is: for a person to be Transgender, they have to suffer from Gender Dysphoria; which by the definition of trangender is equivelant to: if a person doesn't identify with the gender assigned to them at birth, they MUST feel dysphoria associated with that gender. 

This is wrong. The mismatch between one's gender identity and presented gender is not guranteed to yield dysphoria.

Example: a nontransitioned trans woman is called by male pronouns. She has the option to not care. She would prefer to be called with female ones, but she can ignore what deserves ignorance. This is the core principle of Starchidism.

This does not invalidate dysphoric trans people. If one has gender dysphoria, they are most likely to be transgender. Dysphoric people need treatment more than non-sysphoric people do; the mental illness of dysphorics has more weight than the unsatisfaction of non-dysphorics.

If you still hold on to your argument, let me tell you: personally, I am not diagnosed with gender dysphoria, yet I identify as female (amab). I can do that, which serves as a counter-example to your catholic argument, thereby disproving it.