Askeladd to Thorfinn in Vinland Saga. Thorfinn follows Askeladd around in hopes of avenging his father, but whenever Askeladd kicks his ass he offers advice.
In Yaiba, his father Kenjuro ends up training Onimaru in order to fight Yaiba as if it was Kenjuro himself. Unlike other examples, Onimaru did seek for Kenjuro's advice first.
In Attack on Titan, two characters teach Eren how to do hand-to-hand combat during their days in military training. They (plus another character) are later revealed as having been The Mole since before the training. When faced with combat, Eren tells one of them that his biggest mistake was teaching him how to fight before trying to kick his ass.
In the football manga Eyeshield21, protagonist Sena's childhood friend Riku teaches him about the importance of protecting the ball to avoid fumbles... during a match in which their respective teams are playing against each other for a spot in the national tournament. Sena uses this knowledge to surpass Riku during the game, but his team loses anyway.
Occurs in One Piece with Roronoa Zoro and Dracule Mihawk, after the former is willing to throw away his pride and beg the latter for help to both defeat him and better serve his crew.
Isshinai Ogata of Kenichi: The Mightiest Disciple almost actively encourages this. While most of his disciples are respectful, if not reverent, of him, he has absolutely no problem whatsoever if a student turns against him and trains with him with the intent to ultimately kill him, since if they succeed it means that student has surpassed him.
There's this Buffy the Vampire Slayer fanfic Change Partners and Dance. It has Spike arrive in Sunnydale at the same time as Buffy. He ends up teaching Buffy how to fight, if only so that when he kills her she'll be able to give him a real challenge, only to end up falling for her (and vice-versa)
In Star Wars, generally, the Sith knowingly train an apprentice who will eventually betray and kill the master to become the next one.
A large part of 1632 by Eric Flint. There is a policy of spreading knowledge relatively freely all over, especially medical. More specifically, Mike Stearns mentors Wilhelm Saxe-Weimar in how to build an effective and credible opposition to him in 1633.
Caleb Carr mentions this in his 2002 book The Lessons of Terror. The Roman Empire ended up training the "barbarian" soldiers who would later defeat them, including the Auxiliaries who rebelled and destroyed Varus and his legions. I don't believe this was intentional on the part of the Romans, but then I'm not sure you require forethought for this trope.
Subverted in Harry Potter. Snape was ordered to teach Harry legilomancy, and it was an ordeal for both of them because of how much they hated each other. Snape spends most of the series certainly appearing to be an enemy, and he definitely has shades of the Token Evil Teammate, so his teaching Harry, particularly at the end of HBP, probably qualifies, though you might ultimately consider him a subversion.
Scorpius in the 4th Season of Farscape was this to Crichton.
In Noob, it known ever since Season 3 finale / the middle of the third book that the strongest players of all three factions, Fantöm, Amaras and Spectre are going to have a three-way battle to see which of them is the best. Spectre mentors Fantöm both to get to know him better and beacause he wants to fight Fantöm, who's in the middle of recovering from a big blunder, at full strength.
White Wizard handed a guard of Koyomi and the belt from Kamen Rider Wizard after the Solar Eclipse created the Phantoms, he assist and helped in their evolution to many future forms, but the White Wizard himself has create the Solar Eclipse (Sabbath) to revive Koyomi again but to create the ceremony again, that's will coast many lioves, but Kamen Rider Beast broke the act, and after Kamen Rider Wizard fights again with him. Don't forget the White Wizard is the leader of the Phantoms, Wiseman
Edgar Grint: Excellent. Use aerodynamics, not just thrust, to your advantage.
An early enemy in Earthbound (one of the street gangsters headed by Frank, to be exact) explains you part of the combat system just before starting a battle with him. He even lampshades it.
In Zeno Clash, Metamoq trains Ghat in advanced unarmed combat, only to end up attacking him for real and committing suicide via grenade.
In Chrono Cross, during boss fights with Solt and Peppor, you're explained some aspects of the combat system, when they try (and fail) to use those aspects against you.
Big Boss in Metal Gear mentors and supports Snake in his mission while secretly running Outer Haven in the original game. Though we know how that turned out for him. I think we need more context on the mentor's motivations here.
In Metal Gear Solid 3, Naked Snake gives young Ocelot tips and analysis on how his gun is being used, particularly after Ocelot gets his ass kicked by Snake.
Jade Empire: Master Li trains his student this way, introducing deliberate flaws in his teachings so he can exploit them later.
Chase Young from Xiaolin Showdown is this to Omi, continually dropping hints so Omi could become a better fighter. Of course his actual goal is to slowly convert Omi into joining his side.
In Avatar: The Last Airbender , Iroh was about to be mugged, when he notices the mugger's stance with the knife is poor, and ends up fixing his stance. He did this by dodging the mugger's attacks, then quickly correcting his stance mid-stab.
Nations tend to open up their military and non-military schools and such to foreign nations. Thus, if the nations go to war, it happens that some of the people on the other side were trained by their current enemy. The United States tends to give military training to a great many foreign nationals. And of course, foreign students in American universities is par for the course. The British military has found themselves at times facing a native opponent who just happened to be trained by the British army...
There was a law in Sparta that the same enemy should not be fought too often, lest they'll learn from the Spartans how to fight well.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.