A bug in the rules?

Someone on Chess.com will have a greater knowledge than me on this issue.  I figure that I am not the first in the history of the game to wonder if this is some kind of bug in the rules and seek reference to historical arguments on this kind of move.

After white moves the pawn to h3 to hassle my black king, I ask why it is that my Black King can't move up to g3? [Note: Dinkydoe quite rightly points to the white knight on the back line - but ignore it, pretend it isn't there.  Once I master the online board insertion tool, I can update the illustration. ]  

How can I be moving into check when white's "attacking" pawn at f2 is in fact a neutered pawn.  It can't move or it will reveal a check from my black bishop.

Instead I am forced to retreat.  Unfairly I think.

 What are you views on this?

 

UPDATE: so I have made the effort and I know now that a piece that can attack a king, whether they can follow through with the attack or not, puts the king in check. Oh well.  But then it is the philosophy of this rule which so fascinates me.