Well, from someone who has read up on it, it's a bigger problem then you think. Just because tree's grow doesn't mean they always grow back after being chopped down. In fact, half the time, they plain don't grow back, as the animals that once lived in those tree's are no longer their to provide a decent fertilizer for the trees to grow back in.
Plus, most of the time, when they're cut down they do so for the land, so if they put a great big highway through what used to be lush forest, those trees ain't coming back. Yes, a lot of what people say about deforestation is crap, it's not the soul cause of global warming for a start (if anything, we can put that down to the methane produced by ourselves and most cows (those two candidates being the biggest contributer)) and plus freshwater algae produces more oxygen than trees do.
But, one problem scientists seem to have with deforestation is the fact that a good chunk of the Amazon hasn't been explored yet and is slowly being taken away. This means that certain rare plants an animals that live deep in the Amazon forest are being wiped out, and for all we know, such plants or animals could provide a great benefit to mankind (such as cures for certain illnesses and so on). But of course we'll never know if we lose the forests.
As for ice melting not doing **** to our sea levels, you are aware ice floats right? If the ice were completely submerged then yes, it wouldn't make a difference (would even lower the sea levels if they melted), but since there are huge chunks out of the water (like the polar ice caps for instance) then of course it would make a difference. And not just to sea levels, that's a giant chunk of freshwater being dumped right into the Atlantic sea, salt water. If that happened, the salt water would sink and temperatures of the water would fluctuate causing shifts in major ocean currents... not good for our weather.