Why is Ng5 an innacuracy?

https://www.chess.com/game/live/131085545565

Move 9

It's honestly probably due to a lower engine depth. Your Ng5 move was good. At least at my engine depth, it's the second best move and Nb5 is only a super smidge better. Chances are that the lower depth engine considered Nb5 "best" and Ng5 to be however many centipawns "worse" than the best move. I wouldn't worry about it honestly.

Your Ng5 move is logical and threaten to fork everything in sight via Nxf7

For instructional value, Nb5!? is a computer-esque move which aims at advancing pawns while creating attacking threats because both sides have castled on opposite flanks and this usually means both sides may want to pawn storm there.

The line I have is 9. Nb5!? Qb4 10. a4 (securing the knight) a6 11. c3 (ignoring the attacked knight on b5 because pawn capture and recapture on b5 would open the a-file and make that deadly to that black king) Qe7 12. Bf4! attacking c7 or also 12. b4!? with the interesting idea mentioned of launching a pawn storm with an attacking advantage to white.

Since that is a lot of chess notation, I put the line into a pgn diagram too.

Yea looking at it again, you're probably right. The move can simply be countered with Qd7...e7...f6...f8, Rd7...f8, Be6, or Nh6. It's likely why the low-depth computer evaluation didn’t like it.

In general, "inaccuracy" is a pretty good move that's slightly worse than the best. Unless you are on the grandmaster level, you probably should ignore those, and concentrate on more serious mistakes instead.

It isn't an inaccuracy.

Since both knight moves are good continuations in a game which white is winning and since they are really very different from one-another regarding their impact on the game, it's more a matter of taste as to which is played.

It's incorrect to call a good move "an inaccuracy" simply because its impact may not be evident to the engine and it really boils down to poor teaching methods and rather slipshod programming. Any teaching method which downvalues a perfectly good move by a student of chess is poor because it results in lack of confidence both in oneself and in the teaching method.