I have a few close friends and a brother who will be having their first baby soon and I took an informal poll of if they would cut the umbilical cord or not. The results were mixed and if they said 'yes', they would follow it up with a joke like: "I'll do it with my teeth," or "I might go Tom Cruise on the placenta." They had to make a joke to defuse a relatively uncomfortable subject.
Should I feel guilty that I have no desire to cut the umbilical cord for my child? I don't think so. I have never asked my father if he did for me and it would not change my perspective on him. Fathers do little to nothing in the pregnancy or birth, why should I step in to cut the cord of life?