How can Kyo Sohma save Tohru Honda's mom?

Warning!!! Spoilers!! Kyo could've jumped in front of Kyoko (Tohru's mom) to take the hit instead. But he would've collided with her and poofed into his cat form so he didn't move and she got hit by the car and died. Kyo was torn by this and went to the mountains to train and work off his shame.