After black plays Nc6-b4 (threatening white's bishop on d3), I don't understand why Qd1-a4 is not a reasonable response. (It checks the king and threatens the knight--the knight must retreat to block check, or be lost)

Attempting it gets a generic "Save the bishiop or weaken e4."

Could you post the entire variation> I'm not sure exactly what position you're talking about

AKO007 is the lesson #. Lesson title is the topic title.

1. e4 e5

2. nf3 nf6

3. Nxe5 d6

4. Nf3 Nxe4

5. d4 d5

6. Bd3 Nc6

7. O-O Be7

8. c4 Nb4

Attempting 9. Qa4 gives "Save the bishop or weaken e4" with no further explanation. Forcing the knight to retreat with a pin on it would seem to accomplish this. (Though in thinking it through some more, it may not work as well as the correct move, an explanation would be good, I think)

Not actually threatening the knight, the bishop is defending it. Black can just play Bd7 and force the queen away.

I think 9.Qa4 is actually a mistake! Black has the interesting 9...b5!? 10.Qxb5+, Bd7 loses a piece, as does  10.cxb5 Nxd3. White's best seems to be 10.Qd1 Nxd3 11.Qxd3 bxc4 with an advantage for Black

Ugh, tunnel vision. Totally forgot about the bishop guarding the knight.