In what case does a TM move NOT pass down through breeding?

Question

I read the comments on this and it was all very confusing to me. I figured I should ask this question before I hurt myself in confusion.

Answer 1

Prior to Generation VI, if the father knows any moves that are TMs or HMs in that game (and in Crystal, moves that are taught by a Move Tutor) that the baby is also compatible with, it will inherit the move.

source
It says nothing about needing to be an egg move or the mother needing to know the move.

Answer 2

These are the situations that the move IS passed down. It's way easier to write this way.

If a known TM move is an egg move and the father knows the move, then the move is passed down.

If both the mother and father know the TM move then the move is passed down, regardless of species bred.

This can be useful in two situations:
1. Gen 4 and before when passing down TM moves.
2. Teaching a pre evo a TM move taught exclusively to a later evolved form. This can be an advantage in LC. I don't know of any case that this applies to because I don't do LC, but there may be an exception somewhere, and if there isn't maybe one day there will be. You asked a question about this before. Like said then, it would be a tedious study to examine every possible exception.

Comments

But I still don't get why TM moves are sometimes but not always listed as egg moves as well...

---

Ok well read the two rules I wrote in my answer.  Which one is easier to do?  That's why some TM moves were egg moves prior to Gen 5, and after Gen 5 they kept it that way because they didn't have a reason to change it.

So you might ask why don't all Pokemon have it then?  Well that's just how Gamefreak wanted it.  Important egg group bridges have them, so that could the factor that decided which Pokemon got TM egg moves way back when... but unless Gamefreak says so then it's anyone's guess.

---

Darn. Gamefreak logic is getting kind of annoying.

---

I just bred a male Camerupt with flamethrower and earthquake with a female Rhyhorn with neither move, and all the eggs hatched into Rhyhorn with flamethrower and earthquake. I don't think flamethrower and earthquake are egg moves, so how did they get passed down?

---

Were both Flamethrower and EQ taught to the Camerupt?

---

Camerupt learned them by level up.