Why does Via’s dad support her in the argument between Via and her mom about Via riding the subway?

Via's dad understands that she's getting older and needs to take on more responsibilies. He also knows he needs to let her make her own way. Thus, he supports her assertion that she can take the subway for two reasons; he trusts her, and he knows she is feeling let down by her mother..... in that she's taking a back seat to Auggie.

"Isabel, she can take the subway!" said Dad impatiently. "She's a big girl now. She's reading War and Peace, for crying out loud."
"What does War and Peace have to with anything?" answered Mom, clearly annoyed.
"It means you don't have to pick her up in the car like she's a little girl," he said sternly.

He thinks she is old enough and mature enough to go into the subway