Why does my opponent think he is worse?

Why does my opponent think he is worse?

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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?