I had a friend in New York who was always, always comparing her 2 months-younger daughter to mine. It was all she ever talked about. If I would ask about how her life is going otherwise, it was a word or two, and then back to her daughter. I acted indifferent after a while, and slowly I just let the friendship fizzle.
Around the same time, I met a wonderful mom through this site, and her child is about the same age as my daughter. But there is no comparing, no snide remarks, no put-downs. Our friendship exists to support each other and give advice as moms. I don't feel stressed at all when I talk about my child to her, as opposed to that competitive pal in NY, because I know I won't get judged.
I deal with a lot of competitive moms these days, esp that my
daughter is speech-delayed, and small for her age. I try not to let it get under my skin, and act indifferent when people say snide comments. She's getting speech therapy and doing great in her own way.
I agree with the others -- act indifferent or overtly praise her. She is very insecure, and that is why she feels the need to 'show off.' Showing off make herself feel better, because her self-esteem is so low. Perhaps her parent(s) were like that with her.
If her constant comparing still irks you, or she doesn't get the hint, I'd just let the friendship slowly fade away.
There are many more moms/friends out there who would never compare; they'd support you, be happy for you and your child, and never judge. Friendship is a two-way street. Join the local mom's group and branch out and meet other more down-to-earth moms. Go to www.meetup.com to find groups in your area.
The sad thing is, she is teaching her child to be the same way like her. She's setting her child up to be an overachiever, a child who will never be happy with him/herself throughout life, no matter what accomplishments are made.