A woman who wants a man to do the "initiating" and to "take the lead" are women who wish to be pursued and courted, not chased. They are sincere in their desire and seek the same in the man who is pursuing them, and as such, give the same deference and respect to the man as she expects to receive in return.
Women who seek to be "chased" are the exact opposite. Most who look for a man to "chase" them aren't desiring a man to pursue and court them as much as they're looking for someone to cater to them. What is absent from this, however, is the common respect for each other, as "chasing" is based on fleeting interest and desire rather than genuine and deep-seated desire. More often than not, the "chase" lasts no longer than the length of time it took to begin.
And that's why men will resist the urge to "chase", unless they're desperate. A sincere man will give his best effort to court a woman who he believes is also sincere and respects him as a man. However, he will lose interest the moment he starts to believe that he's pursuing a prima donna. He will simply move on to someone he feels won't waste his time playing games, like insisting that he "chases" her.
I, personally, will pursue (to varying degrees) anyone with whom I have a sincere interest, but I will never "chase" anyone. ANYONE.
I like this distinction Victor, and think it's an important one.