Dont understand why the recommended move is rated higher

https://www.chess.com/a/2EQNPom4A2DUr2

Can someone please help me explain mistake nine.  9. d3 Critical move. 9... 

g5? ± MISTAKE (+3.34)

Appreciate any feedback and if there is an easier way to post the game on the forums.  Thanks!

2. ...Bd6 - in most cases not a good idea to block your central pawn in the opening.
3. ...h6 - not really following opening principles, this move doesn't help you develop
6. ...c5 - you might sometimes move c pawn in the opening, but it is not that useful here, not really developing, Bc5 is recommended to unblock your central; pawn and to attack f2 for the second time
7. ...f5 - extremely weakening considering your king is unsafe in the center, pawn pushing without developing - very bad
8. ... 0-0 castling is the right idea, but your kingside is weakened

9. ... Ng5 the exact reason why is this bad is unclear for now, but the problem lies in the fact that your king is unsafe on the weakened kingside and your queenside is undeveloped
11. ...Ng5 the same reason , your kingside is weakened and the only defensive piece you have is that knight, he probably has some attack against your king
14. ...Qe8 - very bad , if he plays Bh5 , the queen is lost, his bishops would be great there
15. ...b6 still not developing queenside
16. ...Bb7 in normal circumstances fine, but you position is bad that this developing move is probably just not good in view of his potential attack against your king

18. ...Rf1 - Not good, probably blocking an escape path for your king - Bh5 if the queen moves he can even sacrifice the rook and play Qg4+, complicated for you at this level, but the idea is that your king is "naked"
19. ...exd4 you could have taken a free knight on e4

I didn't do the analysis in depth, so something might be a bit sketchy but you get the point.  

And now for the tips.

First of all if you wish to improve, here are some general tips that might help you out:

https://www.chess.com/blog/nklristic/the-beginners-tale-first-steps-to-chess-improvement

In order to survive the opening (you might not be so lucky next time, both of you played some questionable moves here) read this if you have the time:

https://www.chess.com/blog/nklristic/surviving-the-opening-first-steps-to-chess-improvement

Finally, if you want to analyze games, and you should if you wish to improve, here are examples on how to do it:

https://www.chess.com/blog/nklristic/how-to-analyze-your-games-first-steps-to-chess-improvement

You don't need to be this detailed in the notes department, I did it this way so people can follow the flow of the games easily.

I hope you will get something out of those articles. Have a nice day.

The quick analysis tool is bonkers. Often I observe one move as a mistake or blunder and proceed to play the recommended move. Lo and behold - the tool claims this to be a blunder - and suggests the 1st move as best!!

It’s all due to depth of analysis- the horizon effect.

A longer/deeper analysis must be made. The caps score is quick and dirty- no stock can be made  of it.

It’s common to see caps under 20 in games with but a couple of inaccuracies or caps of 98+ in games with inaccuracies galore / including mistakes in games of less than 30 moves. 
Danny reported improvements are in the works. They know the tool is leading new players astray - reporting games as cheating by the often meaningless high scores.

Yeah but in his game the analysis tool wasn't wrong, and in most cases it is right anyway. Some odd occurences are to be expected.It is a machine and it sees the game through its cold, black and white, machine eyes. Human eyes are sometimes needed to add some...color.