Would it be strange to want to be underweight?

Depends: Underweight if excessively so is unhealthy. But if just slightly so, it would be fine. Be sure you do not have anorexia however. In the middle ages, being moderately overweight was considered a sign of wealth. But in today's world, slimness is a desired trait. It is even more important to be physically fit however.

It depends: A light-boned man who is very well-trained for track-and-field, where aerobic fitness is a plus and muscle mass is a minus, will be "underweight" according to the tables. It's fine. Another person may wish to look undernourished for whatever reason, perhaps a body dysmorphic disorder, and can make themselves sick doing this. If this is anorexia nervosa, it's dangerous. Best wishes.