Why should we feel sorry for Walter Mitty? Why or why not?

Whether or not the reader feels sorry for Walter Mitty depends on whether or not they think he is happy and content. It is possible that Walter chooses this life for himself so that he can disappear into a world of fantasy when and where he wants. Unfortunately, the suggestion is that he dreams up all these adventures, of course making himself the hero, to block out how much he dislikes reality and how everyone seems to be trying to control him. For example, his wife nags and berates him:

“Remember to get those overshoes while I’m having my hair done,” she said. “I don’t need overshoes,” said Mitty. She put her mirror back into her bag. “We’ve been all through that,” she said, getting out of the car. “You’re not a young man any longer.” He raced the engine a little. “Why don’t you wear your gloves? Have you lost your gloves?” Walter Mitty reached in a pocket and brought out the gloves.

A policeman at the traffic lights tells him rudely to hurry up:

“Pick it up, brother!” snapped a cop as the light changed, and Mitty hastily pulled on his gloves and lurched ahead.

And, finally, a woman laughs at him for talking to himself:

“Puppy biscuit,” said Walter Mitty. He stopped walking and the buildings of Waterbury rose up out of the misty courtroom and surrounded him again. A woman who was passing laughed. “He said ‘Puppy biscuit,’ ” she said to her companion. “That man said ‘Puppy biscuit’ to himself.

The reader knows that Walter is not happy with all this, because after the parking lot attendant patronizes him, he says to himself,

They’re so damn cocky . . . they think they know everything.

While the writer doesn't give away too much about his life and character outside this short shopping trip, he does seem to suggest that Walter is your stereotypical henpecked husband with very little going for him outside his marriage. Whether or not a reader empathizes with this type of character depends on their own belief system. Like all great stories, this one is open to interpretation.
https://www.newyorker.com/magazine/1939/03/18/the-secret-life-of-walter-james-thurber