He kicked your butt on the climbs because he has a better power to weight ratio than you do. That's not so much about VO2 max as it is sustainable high power output and body weight. Men generally can produce more power than women.
If he also kicked your butt on the flats, that's more an indicator of VO2 max - or absolute sustainable aerobic output with the power/weight variable taken out.
Training can help you increase your power output, not doubt. VO2 max may or may not be "trainable" - to a certain point, there are genetic limitations that cap VO2 potential in a way that make it less "trainable" than power output, as you alluded to. Whether more training will help you, who knows. I don't know what sort of training you have been doing, how long you have been riding, etc. Often it is not more training, but better, more focused training that can help.
If there is a facility near you that can test your lactate threshold levels and design a training program around those, that would be highly recommended if you are serious about the scientific approach to training, which it seems like you are. I've had a series of those over the years and they are very helpful for setting training targets for interval training (to build power output) and also to help target thresholds for long endurance rides. I highly recommend a program like this.





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, I'm having problems gauging how much to eat and train... to lose those #s.