But why are you using the big ring for climbing anyhow?
It's not bringing you any advantage.
Quoting myself from above: " A 39/53 crank together with a 12-21 cassette on a 28"/700C/622 mm wheeled bike should give you a comfortable speed range of around 13-25 MPH on the small ring, while the speed range on the big ring is something like 18-35 MPH"
For an inexperienced solo rider, most of your riding should be on the small ring. The only times you can put the big to good use is in a wicked tailwind or on a serious descent.