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"Convincing" someone is something you do over what film to see, or, at most, what apartment to rent - NOT whether or not to have a baby.
I can't imagine giving up the love of your life over kids, as he suggests is possible - does he realize how fortunate he is to have found what he has now? How few people find anyone that great and perfect for them?
And yet he wants MORE.
He wants her to 'change' when HE wants things to change. He wants her to want a baby suddenly, although she never wanted one before - did he assume that she would be like the 'stylish women' he mentioned, who overnight realize that they want motherhood?
If someone doesn't want kids, "convincing" them otherwise is a selfish, destructive idea. People who are 'talked in to' wanting something don't really want it - they are being conciliatory at worst, hopeful that their own feelings will somehow change at best.
If she doesn't want a baby, do her the honor of taking her opinion and feelings seriously, treating her attitude respectfully - and stop treating the issue like some 'game' that you want to win.
(even though you yourself aren't sure about kids, either...even worse)
None of the reasons you list for having a baby are good reasons - you only talk about crap like handing out orange slices as the oldest father, about what your friends want, about the family name. Nowhere do you talk about how great it would be to PLAY soccer with your kid, how great to enjoy his/her company, how great to watch them grow - all of your stated reasons are narcissistic or about peer/social pressure.
Those who don't have kids are not genetically inferior, as some here suggest - they are simply better at resisting biology, or less susceptible to biology. In fact, people intelligent enough to separate a biological urge from intellect, and give the 'urge' serious thought, are examples of finer humanity.
Get off her back. If you are dumb enough to dump a great love over some mindless urge to procreate and a few social pressures, you don't deserve her anyway, sweetie. You sound like a nice guy, but you are unrealisitic about what parenthood is, and how you are looking at the issue is sophomoric and simplistic.
Has it occured to you that maybe you fell in love with a woman who doesn't want kids because you aren't meant to have any?