Peter Walsh seems more like a free spirit, or maybe, never wants to grow up when it comes to his life.
In a way, he is a romantic. Reading through his romance, we can see that he loves with his instinct. When he feels right, he goes for it. For example, his marriage with the girl he met on the way back to India, or his love affair with the married woman. Somehow this free attitude still attracts Mrs. Dalloway. She sees the flaw of his characters, but she is still attached to this person. Peter fears aging, and he still love the idea of being young. I think when he is being judgmental towards Mrs. Dalloway’s sophistication, such as scolding her being a perfect hostess, is another way of showing that he is scared getting old(being responsible, be social in order to have that status in society). Yes, he seems happy with his philosophy of life unlike Mrs. Dalloway. Though the fact that he is not the one that Clarissa chose to marry just shows his main struggle of life: being independent and responsible.
In another way, Peter is impulsive and irresponsible. “He had never done a thing that they talked of; his whole life had been a failure. (6)” Failing Oxford, never seem to make a serious commitment, and the fact that he is very judgmental about the world all shows his immaturity. He barely follows through his passions or has a plan for his life, as Hugh Whitbread says his character is “permanent” (105). I think it is the youth from Peter Walsh that makes Mrs. Dalloway still thinks about him often. She misses the way they interact with each other and the youth/beauty of their love; she also misses the way that he is not afraid of staying young (even if it is immature). For Mrs. Dalloway, his way of living life freely assembles something young and vivid, something more like a hope that she wishes she never loses. Although we know how life wears her out when she becomes this mature and sophisticated Mrs. Dalloway.