That's a really unique twist on the explaining.......
i may use it for one of my stories 
The magic system in a story I'm writing lets you learn magic abilities faster if you're bonded with someone. The people of that world tie a lot of culture and emotions to their magic and the bonds they formed to get them.
The main character bonds with people who are oppressed because of their magic type, and wants it to be known who gave him that ability, both so his enemies know they are hurting real people, and so if he dies they know who he died for.
Others seek to master one ability, and form teams with others who know the same ability so they can collectively perfect it. They form their identities around their shared ability, taking great honor in them and going on quests together.
Another reason people say their ability is because most people travel in groups in this world so they can grow their bonds and be stronger together. Saying their abilities helps their friends or followers learn the move even faster, and again its usually said in pride. Some people like saying the names of their abilities out of respect to whoever gave it to them or to show they are part of a specific school of magic.
There is one character that takes advantage of everyone's acceptance of being honest about their abilities and outright lies about what her abilities are lol. Another character is excited for everyone to know what he can do, even if they're an enemy. Most characters never say what their ability specifically does, but usually, the name of their ability carries some weight for them and helps grow their bonds, and they wish to honor it.
making such explanations a cultural aspect can be interesting, specially because it can be a way to encourage the following of certain schools of magic, just like some martial arts schools make public demonstrations.....
Yeah 
It carries a sense of pride and "you totally want my ability now" with it. Or a sense of justice for the main character who fights with the abilities of the oppressed.
Then stuff gets sad when an ability dies out and all the history surrounding it. Or if the bond you had is broken, that ability get stunted or completely forgotten.
that reminded me of a character from Hunter x hunter who made explaining his abilities a requirement for his power because abilities can be empowered with restrictions and because he used those circumstances to blackmail people affected by it.
They were cursed by a witch to always explain their powers. Valid.
In all seriousness... To add, I think it'd make sense with a strong person vs weaker person dynamic. If the weaker person has no chance of gaining any advantage even when they do learn the explanation, the stronger person has no reason not to explain it apart from personal reasons (unless the weaker person could get back to someone else who's stronger, who would then use the knowledge). This has been done before in some anime and manga, and it should be in-character. Sometimes the stronger person is humoring the weaker one, toying with them, other times they pity them and they're being nice so they explain what is going on.
by the way.....i've seen random clips of fights from Jujutsu Kaisen and it's freaking awesome!.....guess i should start watching it
The person explaining the ability does no only because he is confident, but wants to humiliate the victim by telling them how powerful the technique is, thus how beyond anyone else this person is.
This for a villain of course
Let them explain their powers but lie, like they may say
" I have fire powers, and i couldn't function near water"
So if enemy was smart, they would put them in big bodies of water, then character can defeat them and admit to lying , and just before killing them, actually saying/showing their powers
and to stick further into the wound the character may say: "you really thought i would be foolish enough to tell you my ability and weaknesses?"
Why not just lie tho lol.
"Hey, yeah, so i have fire powers. I touch water and i die."
Villain dives into a water body with them "Aha!"
"Sike bro i'm actually half mermaid i love water. Behehehehehehehehe thanks."
I had to think for a while since seeing this topic. I've come to the conclusion, that there is no justification for explaining powers to an opponent in combat. It's at the worst a bloated narrative tool, and at the least a poor tactical decision.
Edit: HXH is pretty much the only series I've read that managed to make this trope work. But even then, it's a bit of a slog to read through.
I prefer to let the readers figure out how powers work over time.
Hunter X Hunter often takes interesting angles because such explanations are rarely done to enemies.
-Explaining their ability is often done between allies to optimize teamwork or as a sign of trust.
-There is a nen user in Greed Island who does this as a requirement for his ability and as a result, said ability has a massive boost in power.
-Hizoka's memetic explanation of "bungee gum has the properties of rubber and gum".......makes his ability sound ridiculous until he uses it for many creative and deadly tricks.
Which is mostly because Togashi himself dislikes the tropey nature of Shonen comics, so he actively changes up the formula.
But anyways, I'm not writing a Shonen series so it's a moot point xD. If people really want to know how powers work in my series, they can wait until I do Q+A's and I'll answer them lol