I concur, I would not permit the cross-class, or rather, I would make it a case by case basis.
Could a Wizard "teach" an Arcane Trickster or Eldritch Knight? How about someone with the Magic Initiate feat who takes Arcane spells? Are you going to let Bards "teach" a Cleric or vice versa? How about a Cleric "teaching" a Paladin? Paladin teaching a Druid?
I think this is a can of worms that, if you want to open them for roleplay/story reasons, have at it. But I would have a well structured "funnel" to pour that can into as soon as it's opened.
1. My primary question would be...What kind of magic are we talking about?
In my own game world, I draw distinctions between Arcane, Divine, and Nature magic. For the purposes of 5e/BTB, we have to look, at least, at drawing lines between Divine and Arcane.
If "Yes," then that's one hurdle down. Proceed to #2.
So, theoretically, a Sorcerer could "teach" an Eldritch Knight (though I would say the "figured magic out on my own/how it works for me" fluff of a sorcerer would prohibit this from an immersion/believability pov). An Arcane Trickster could teach a Bard (though in my game world, this would be a no since Bards are NOT arcane casters).
If No, then sorry. No way. A Paladin can not teach a Wizard. A Warlock can not teach a Druid. A Bard [per 5e] can not teach a Cleric.
2. Is the spell shared on the different class' spell lists?
If Yes, then let them do it.
So, Clerics might [if the spell appears on both lists] be able to teach a Paladin. A Wizard might teach a Bard (per 5e) or Sorcerer ...my immersion hackles go up at the idea of vice versa. But, if we're keeping this simple, that should/would be allowed. etc...
If No, then no dice. Won't work. You could rp the attempts at instruction (might be fun), but it's not going to work.
2a) In the interest of internal consistency, for me, I would add: Are the schools of magic a match, as well?
So only abjuration/evocation spells could be learned by an Eldritch Knight (since, btb, those are the only schools the EK can learn). Only an Illusion or Enchantment could be taught to an Arcane Trickster...and vice versa. Because those are the only types of spells/kinds of magic these subclasses have a knack/talent for/interest in. If you wanted to go the extra mile, for flavor, you could stipulate that only those types of mages, Abjurers/Evokers/Illusionists/Enchanters, respectively, could "teach" the subclass properly.
Back in the [1e] day, "sharing spellbooks" was a relatively common practice among party mages who were of suitably similar alignment/outlook/pragmatism. Sometimes not. But most of the time, it was good for bolstering both casters' versatility.
If you wanted to say, due to the nature of their training and widespread spell selection, that a Bard (and ONLY a Bard) could teach cross-discipline, that is...believable, I guess. They get a few spells from here, a few spells from there, a coupla magical secrets, etc... Sure, if the spell appears on both the Bard and the other class' spell list, go ahead. Again, it wouldn't work for me/in my game world since Bards have their own, completely separate, casting style (more like a channeling than casting, really) but if you're just doing run-of-the-mill-PHB arcane-full-caster Bards, I suppose it is plausible.
But the "open door cross-class" idea, to say "ANY class can teach a spell to ANY other class", is just a biiig No-no for me.
Could a Wizard "teach" an Arcane Trickster or Eldritch Knight? How about someone with the Magic Initiate feat who takes Arcane spells? Are you going to let Bards "teach" a Cleric or vice versa? How about a Cleric "teaching" a Paladin? Paladin teaching a Druid?
I think this is a can of worms that, if you want to open them for roleplay/story reasons, have at it. But I would have a well structured "funnel" to pour that can into as soon as it's opened.
1. My primary question would be...What kind of magic are we talking about?
In my own game world, I draw distinctions between Arcane, Divine, and Nature magic. For the purposes of 5e/BTB, we have to look, at least, at drawing lines between Divine and Arcane.
If "Yes," then that's one hurdle down. Proceed to #2.
So, theoretically, a Sorcerer could "teach" an Eldritch Knight (though I would say the "figured magic out on my own/how it works for me" fluff of a sorcerer would prohibit this from an immersion/believability pov). An Arcane Trickster could teach a Bard (though in my game world, this would be a no since Bards are NOT arcane casters).
If No, then sorry. No way. A Paladin can not teach a Wizard. A Warlock can not teach a Druid. A Bard [per 5e] can not teach a Cleric.
2. Is the spell shared on the different class' spell lists?
If Yes, then let them do it.
So, Clerics might [if the spell appears on both lists] be able to teach a Paladin. A Wizard might teach a Bard (per 5e) or Sorcerer ...my immersion hackles go up at the idea of vice versa. But, if we're keeping this simple, that should/would be allowed. etc...
If No, then no dice. Won't work. You could rp the attempts at instruction (might be fun), but it's not going to work.
2a) In the interest of internal consistency, for me, I would add: Are the schools of magic a match, as well?
So only abjuration/evocation spells could be learned by an Eldritch Knight (since, btb, those are the only schools the EK can learn). Only an Illusion or Enchantment could be taught to an Arcane Trickster...and vice versa. Because those are the only types of spells/kinds of magic these subclasses have a knack/talent for/interest in. If you wanted to go the extra mile, for flavor, you could stipulate that only those types of mages, Abjurers/Evokers/Illusionists/Enchanters, respectively, could "teach" the subclass properly.
Back in the [1e] day, "sharing spellbooks" was a relatively common practice among party mages who were of suitably similar alignment/outlook/pragmatism. Sometimes not. But most of the time, it was good for bolstering both casters' versatility.
If you wanted to say, due to the nature of their training and widespread spell selection, that a Bard (and ONLY a Bard) could teach cross-discipline, that is...believable, I guess. They get a few spells from here, a few spells from there, a coupla magical secrets, etc... Sure, if the spell appears on both the Bard and the other class' spell list, go ahead. Again, it wouldn't work for me/in my game world since Bards have their own, completely separate, casting style (more like a channeling than casting, really) but if you're just doing run-of-the-mill-PHB arcane-full-caster Bards, I suppose it is plausible.
But the "open door cross-class" idea, to say "ANY class can teach a spell to ANY other class", is just a biiig No-no for me.