Important information you have provided
In fact, when I first met her on the cougarchats site .....
Here is the important information you have provided.
I knew she was older than I, but I didn't realize the disparity in age until she told me (which didn't happen until a couple of dates into our relationship
...
How can I reply to this and win her round ?
Basically the way the situation is now, it can not work out.
She is a cougar (I like cougars a lot, problem is I got older, so technically they are not longer cougars, since I am older then they are

). Generally speaking a cougar is a older,professional,attractive woman who does not really want a relationship, or if she does it is more of an "equal" type relationship. In the Philippines this is probably harder to understand because of the culture. Also usually cougars are more sexually experienced and liberated. She doesn't "need" a man.
You on the other hand are treating her like some sort of stupid 18 year old bimbo. Playing the courtship rubbish, "dates" and crap like this.
Possibly she just wants a "fling" or a more casual relationship. But she also might be concerned you want something more then that. Also she might be afraid if you "fall in love with her" she will hurt you.
I had lots of "flings" with cougars when I was younger. Basically when things started getting serious, main when I wanted things to get serious, it fell apart.
Probably in this case, I would say either move on and find a new cougar.
Or maybe you should not go out with cougars, since you seem to want a more traditional relationship.
Or maybe be less serious with this relationship.
Instead of actually "dating" go and do things together. Be friends with benefits

Hmmm maybe I should go to cougaronline dating site, but I have problems passing as under 35 on a good day
