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.