Why does my opponent think he is worse?

With the Singapore Grand Prix just a week away, it was fitting that my Round 2 game in the thematic Caro Kann tournament verged on an endgame race.

 

I was White in the following position when my opponent offered a draw.

 

One's first reaction when your opponent offers a draw should be "Why does my opponent think he's worse?"

 

If anything, I prefer Black due to his active King. He can induce g3 via ... Kg5, after which he plays ... f7-f5-f4 weakening White's h-pawn.

 

Draw offer made with White to move

 

Analysis I made leading to me accepting the draw offer

 

Game Annotations and Analysis

 

 

Opening Question to follow up

 

 

In this rare g6 setup, what is White's best plan?