In my experience, women
do want to be chased.
Paradoxically, however, chasing them usually makes them lose interest or attraction, as intrigue often grows with time and space.
They will tell you they don't like games nor men who play hard to get, but women want a desirable man that is not easily had. If you chase a women to the point she perceives you're devoting so much of your time and attention to her early on, it signals neediness and a lack of options. If she's not needy herself, this will tank her interest level.
It's also important to distinguish a man
chasing versus
pursuing.
The difference between the two being the ability to lead and the apparent interest level of the woman.
I see
chasing as a guy who can't take a hint or read a woman well but continues to think he has a shot at her, or a clingy guy who initiates everything from a place of neediness. A guy who puts too much time and attention into a particular woman. If a woman perceives you're more needy than she is, not only will her attraction drop, but the power dynamic shifts in her favour and we have enough stories on here to know how that will play out.
On the other hand, I see
pursuing as a man who sees something that piques his curiosity and he takes action to approach because of it. He is operating from a place of boldness, security, desire, and a willingness to lead. After the first few meet ups, he will continue to lead the interactions,
but he won't chase if he smells low enough interest.
Regarding women chasing men, in my experience,
only needy and neurotic women chase and initiate the majority of interactions.
It's normal for a women, once invested, to occasionally initiate conversations. But if she feels like she has to "chase" a relationship, and she's a secure women, she is going to lose interest -- because the man either isn't leading or obviously isn't too into her. In any event, her energy and time would be better placed elsewhere.
@BeExcellent probably would say something similar along these lines.
A secure, higher quality woman with options wants to be pursued by a man who displays interest in her and can lead.
A needy, insecure woman wants to be chased and her neuroticism will cause her to inadvertently do it if you give her enough space.
TL;DR:
Gauge a women's interest level by her
receptivity, not her level of initiation -- especially early on. A secure, interested quality women will be receptive to your leadership when you take action and pursue. A needy, insecure interested woman will "chase" -- she needs the validation
now, hence the initiation.
Every interested chick that chased me turned out to be needy or eventually displayed major red flags, low quality. The higher quality chicks that were interested in me required a bit of work, effort, and the ability to lead in my part. Nothing easily had is worth having.
Women seduce; men pursue.