I educate male children in my realm with high martial teachers. Females are educated in diplomacy or being a steward, because those have a fertility bonus.
Sometimes I remember I should have a good spymaster so I educate a few children with good teachers of intrigue. Sometimes I don't and Poland's spymaster has eight through fourteen intrigue skill.
I find it quite common for randomly generated Bishops to have 20+ learning, so I don't educate children in that unless one is destined to become a Bishop at some point as a way to remove them from the line of succession. To be honest I don't know what benefits it brings to educate will-be bishops in learning instead of steward. With steward they might make more money to improve their holding or spawn more children before being elevated to bishop unless theocratic holdings are different and make better money from having learning or affecting technology throughout the whole county. I ought to remember to grant bishop inheritances to really old members of dynasties I like who are less likely to make more dynastic members, but then again I could simply marry them to a lusty young stewardess from the other side of Europe and have them make as many dynasty members as possible.
Shortly after that screenshot a Duke and a Duchess tried to pass the King of Poland title to Kielbasa's brother, Pizza, who is their fellow Duke and who is visible in the screenshot. Pizza had 100+ relationship score with the King, the faction leader had 40ish I think, and the Duchess didn't like Kielbasa due to being ambitious and slightly foreign. Pizza had around 26 martial skill. They had 120% of Poland's possible levies at the start of the war. I'm not sure how that happened, maybe one hired some mercenaries? My available levies were very worn down from fighting pagans too, so that's more likely. Kielbasa had only one alliance, with his mother, the widowed one county Queen of Aragon.
The Ducal faction declared war following successful but costly wars against Lithuanian pagan states in the attempt to form the Wendish Empire. Poland had gold only for the cheapest of mercenary bands, and mustered a smaller force which lost it's battle against the Ducal forces. It did deplete the Ducal army significantly, by almost half, due to the Ducal army having to cross the Vistula river to reach Kielbasa's army. Just as I'm watching the Ducal army of 7000/12500 or so lay siege to counties bordering Kracow, the Empire of Cumania decides that was a good time to take a few border counties that one of their Dukes has a de jure claim on.
I decide to keep playing as it's Ironman mode, and see what can happen when you lose the big title of the realm to a faction.
The thing that saved Kielbasa is that his aforementioned mother, the Queen of Aragon, managed to die at that opportune moment and left him an inheritance of over 450 gold. I had hidden what remained of Kielbasa's army in the Holy Roman Empire and reinforced it with whatever levies I could raise from loyal holdings. While the Ducal army was deep in a siege in a neighboring county, I hired as many mercenaries as I could afford for a very short while. This consisted of fleeing Kracow and then consolidating with the surviving army, and then marching to the Ducal army. The resulting victorious battle was so bloody for both sides that the cost of the several mercenary bands' upkeep was reduced enough that I didn't have to release them as I thought I would. Peace was quickly offered and titles revoked from non-dynasty members as appropriate.
I then hired both Catholic holy orders available at the time as they have an initial cost in piety and no upkeep when defending against non-Christians. This led to Cumania losing very badly to a mix of holy orders and depleted mercenaries with a few Polish levies mixed in. The Cumania Duke with the claim which started that conflict decided to declare Independence from Cumania after that debacle and I took the other Counties in that Dukedom as Cumania's peace treaty no longer applied to him.