@ZeonII Regardless of your background in martial arts, I think you're wrong there. In fact, arguments of authority are by definition invalid.
First: the objections you're levelling at capoeira as a dance styles are
exactly the same we see in chapters 13 and 14 levelled by South Koreans against their own national martial art, taekwondo. So if capoeira is a dance, so is taekwondo.
In fact, because very few people outside of bodyguards, military and law enforcement officers use martial arts for… well, martial ends, many, perhaps most of them evolved in contemporary times into fitness routines, performance arts and acrobatics. Like another martial artist said in the comments to another chapter, karate and other arts aimed to incapacitate your opponent, so going for vitals and even things like the eye were not beyond the pale. He even said that a local back-alley brawler who knows martial arts is more dangerous than a regional champion who practises in a regulated environment. Makes sense to me.
Back to capoeira: yes, nowadays it's a fitness/dance/acrobatics hobby for most practitioners. But just as taekwondo has a functional variant that aims to defeat an opponent, so has capoeira. If you read the wiki, several MMA prominent fighters, Brazilians and not, are listed whose background is in capoeira, and an example is given of one who used it to decide a fight.
(I don't watch MMA, but from what I hear, its practitioners would laugh at your assertion: for them, what it matters is that it works, so they'll mix - thus the first M - all styles they feel drawn to to achieve their results, be it capoeira, karate, taekwondo or boxing.)
I can mention a local figure in Brazil from the early 20th century, known by the alias Madam Satan. He was a famous drag queen from the Rio de Janeiro suburbs, whose life was depicted in films. He had a colourful life, not less for his legendary mastery of capoeira, with which he famously defeated several cops trying to arrest him, in more than one occasion.
Which is no surprise, because capoeira was developed by black slaves, who used it in fights against each other and in attempts to escape captivity. So maybe you had a bad instructor, or maybe it's just not easy to find a capoeira circle that's focused on the fighting aspect, but it doesn't mean it doesn't exist. In fact, capoeira was taken so seriously that it was outlawed in Brazil after abolition, and only after the laws were relaxed in the 1920s did it enjoy a rebirth.
(Or perhaps it's just that your background is Kyokushin, which never ceased to be martial, as we saw in the Yeon Woo fight. Frankly, it doesn't matter, but you can be excused for your flawed perceptions if that is the case.)
Like said in the note, it makes little sense to call BJJ
the Brazilian martial art. It's controversial even if Brazilians introduced any innovations to fighting routines already extant in judo, which was known back then as "Kano jiujitsu" (Hélio Gracie said he didn't hear the word judo till the 1950s). But even if we grant that BJJ deserves the B, it's barely 100 years old and is an offshoot of judo. So at most,
a Brazilian martial art. Capoeira can be traced back to the 1600s and while it evolved from African roots, there is no such a thing as capoeira in Africa. The time of divergence means capoeira is far more distinct from any conceivable ancestors than BJJ is from judo or other forms of Japanese traditional martial arts (jujutsu).
Therefore, whether you like it your not, capoeira is a martial art (though less formalised than the East Asian ones), and it is the one that has the foremost claim to being Brazilian.