Personally, I feel weird for a lady to shoot the shot. Though I've had multiple bullets from ladies, it doesn't always work out.
It is better for a male to do the shooting, then both will work towards achieving a successful relationship.
The lady leaving it to die off means that she was acting as a result of fluctuations and not love. If she truly love the guy, she wouldn't leave the relationship entirely to the male but instead, she will understand that keeping a relationship is mutualistic and not one sided.
True, but you forget that they're not yet in a relationship. Which is why I said he should go ahead and tell her how he feels and not leave things to chance.