I know insecurity is very unattractive, I can't think of any dating add that says insecurity is is desirable. However, the truth is we all feel insecure about something, you could empathise with these girls insecurities about their weight, by looking at your own.
I am generally a very confident person, but not all the time. At present, I am a bit insecure about my age, whilst I don't look, or act it, I am 50. A girl of about 20-22 hit on me the other day, when taking her home in my taxi. My initial thought was she wanted a cheap cab fare, but she had already paid. So what was I worried about? Well, it did seem a little odd to me that she said she finds older men attractive, what was her motive?
Now look at those girls, they probably think something simular. Why would a man find my fat attractive, when they have been bombarded with reasons as to why fat is ugly. Could it be that he thinks I will be an easy lay etc, etc.
In this day and age, anyone who has never had any insecuities is just arrogant.
13 years