Talking about what's happening in both the Atlantic ice sheets and the Antarctic ice shelves can become complicated, and as far as I can tell (someone please correct me if I'm wrong) not definitive by any means.
However, rainforests are by no means the "Earth's inhaler of carbon dioxide (and by extension I took that to mean 'oxygen producer' as well)". According to many sources (http://en.wikipedia.org/wiki/Rainforest#Tropical, http://www.columbia.edu/cu/21stC/issue-2.1/broecker.htm, http://www.iub.edu/~act/files/publications/1992-93/93-03_Def...), rainforests do not contribute much to global oxygenation.
In fact, organisms like the prochlorococcus http://en.wikipedia.org/wiki/Prochlorococcus have been theorized to be responsible for at least 50% to 60% of the world's atmospheric oxygen (http://www.nature.com/nature/journal/v424/n6952/full/nature0... there's a paper in the references there which has that statistic, but I don't remember which). Today, these microbes are still hard at work, churning out oxygen and while some mistakes have been made (iron seeding, etc) they're still the most populous microbe on the planet.
I would also contest the point about human beings. (This is my opinion talking now). I will not disagree that the earth's climate is changing rather rapidly (relative to the measurable past). I will argue though that it is arrogant to presume that humans are the root cause. On a micro scale, humans have been rather destructive to specific ecosystems. However, I have yet to see convincing proof that humans can effect climate change to this magnitude on a macro scale.