In my experience, that's the message behind a lot of gender inclusiveness. The "Genderbread Person" that was referred to earlier in the thread is an attempt to capture this:
The Genderbread Person v2.0
I've seen various versions of that before. That one is nonsense. "Asex" in the "biological sex" category, for one.
That's not even possible!
That's a good example of how identities, physical sex and behaviors/expressions are being conflated together and it's making a huge mess out of everything.
Interestingly, in the gender inclusiveness training that I've had myself, the instructors gave almost exactly this message. There was a central theme through the whole thing: don't assume. If you need to know how a person sees himself/herself/themself/etc., ask.
I don't know what the course you took entails so I can't comment on that. I'm commenting on the matter at hand in this thread and the sort of thinking reflected in things like that "genderbread" person you posted.
If you want to refer to yourself - and have others refer to you - as a transsexual man, that's fine, but I'm not sure why it should be a problem if some other transsexual man or woman refers to themselves as "transgender". I don't think the terms "transgender" and "transsexual" are mutually exclusive. IMO, there's a lot of overlap.
... though at the same time, I generally tend to respect the terms that the specific person wants me to use to describe them. And I'm not sure why that's a bad thing.
Transgender and transsexual ARE mutually exclusive terms, by the very meanings of the terms.
Trans = across, beyond, on the other side. In the context of gender and sex, it means that you're crossing from one to the other.
Gender = psychological, mental and brain sex. This is your innate perception of self as a man/male or woman/female.
Sex = physical sex characteristics. It includes your genitals, reproductive organs, whether you have breasts or not, hormones, chromosomes, etc.
To "trans" "gender" is to change your gender. Since you can't change your gender identity, this will mean to change your gender role and the way that society perceives you as either a man or a woman. Basically, these people just want to live as the opposite sex but not take hormones or have surgery. Or they may take hormones and perhaps have breast augmentation but not have genital surgery. All or at least the majority of them have a strong aversion to genital surgery and view the other medical modes of transition as optional. Full time cross dressers may or may not fall under this category, depending on the individual.
To "trans" "sex" is to change your physical sex characteristics to match your gender identity/brain sex. Here, there is a strong need to not only change how society perceives you but to also change your physical characteristics to fit how you perceive yourself, thereby aligning the body with the mind/brain. Hormone replacement and sex change surgery are viewed as musts. There's usually a strong drive for genital surgery but various practical considerations such as cost and fear of a botched job may lead transsexuals to putting it off. However, there still exist genital dysphoria.
I am a transsexual, not transgender. Feeling at home in my body is more important to me than just social acceptance as what I proclaim myself to be. There is a lot of confusion and ignorance over the difference of the terms and the different groups they describe. There's a lot of fighting between the different groups thrown together under the "trans umbrella" because of this.
This explains it:
Transgender Paradigm Debunked | Debunk Transgender Myths; Distinguish Transsexuals and Transgenderists
When it comes to that, the real problem is misrepresentation, appropriation and trying to redefine terms to make them mean what they don't. There's nothing wrong with wanting to live as the opposite gender but not change your sex. If you want to present as and live as a man or a woman but not get on hormones or have surgery, fine. But they're not transsexuals. To put it another way, transgender people are fine and even happy being a blend of male and female. Transsexuals aren't and desire to just be male or female. Since science isn't advanced enough to make a transsexual fully a male or a female, we are forever caught inbetween and will never have a fully male or female body and so have to live with that distress although hormone replacement and surgeries can bring us close to our goal. That's the real difference between the two.