Should we try to extinguish all desires?

What are the fundamental claims? For example, in Buddhism the goal is to extinguish hunger, extinguish desire. I remember talking to the first woman monk who was from Thailand to be ordained into the Buddhist priesthood but Thai Buddhists do not ordain women so she went to Sri Lanka to be ordained and she has a PhD in philosophy from McMaster University in Hamilton Ontario and Waterloo. I guess Ontario Mcmaster did a university there. Got her PhD in philosophy and she gave me the first interview. We chatted for well over an hour one-on-one and I sort of angled into some questions because I didn’t want to be too discourteous. And one of the things I said to her is “I hear you’re married” and she said “yes”. I said “You have children?”. She said “yes”. I said “but you’re living in a temple by yourself”. She said “yes”. I said “do you not see your children?”. She started crying. She said “I have a car.” I said “you have a car?” She said “yeah”. I said okay so she drove herself because she can’t allow a man to drive her. She said so she has to drive herself and she says every evening at the end of the day I try and meet up with one of my children. She said “this is the hardest part of my life.” I said “So you are on the journey to extinguishing the desire to be with your children. Is that right? Is that a fair assessment?” She kept quiet and then I said “The dalaI lama has as his primary pursuit now the freedom of Tibet.” She said “that’s right”. I said “why does he desire that?” She looked at me and she said “We try not to get into these philosophical questions. Let’s just say that he chooses to.”