Human life matters far more than biomass and forest coverage statistics. Non-human life is less valuable than ours and is under our administration; it is ours to use for the betterment of our species. Of course, as responsible stewards it is our duty to make use of it carefully so future generations won't be deprived by overuse. And as sensitive stewards we can appreciate the beauty of nature and recognize that some non-human life can feel pain, and adjust our rule over nature accordingly. But the life of some common tree is not worth more than the life of a human; it is not even worth the same.
You can cut down thousands and thousands of square km of virgin Amazon land and you'll still have enough untouched rainforest for every purpose you can think of. The new open spaces have housed wave after wave of settlers adding up to a population in the millions with major urban centers housing international airports and industry. Further south, the acidic soil of the central South American savannah was defeated and its neverending empty flatlands were turned into a global-level breadbasket with several neatly planned cities, a victory of willpower and reason over vacuum. If not for deforestation, most of those settlers would now live in overcrowded eastern slums. Is that really a better way of life than living as a pioneer in a plot of deforested land? Millions of Europeans left their overcrowded continent to build something new on the other side of the Atlantic for similar reasons, and the conquest of the Amazon repeats this on a smaller scale.
And then there's the problem of national sovereignty. Would you feel comfortable with a sparsely populated porous border thousands of km long with several unstable states? That's what the northern border is. FARC guerillas have crossed into Brazilian territory before. Only a populated Amazon guarantees a safe border.
"It's all greed", you might say. It is true that greed is not the ideal driving impulse for the conquest of virgin land, and sadly it's a driving force. But the economic use of conquered land is not evil per se. It is easy to think so in a Scandinavian country where further economic growth brings little improvement to collective and individual well-being. But that does not mean material prosperity is unrelated to happiness. It just has diminishing returns. As an undeveloped state we are still at a point where economic expansion can have social/imaterial benefits. And within a globalized economy, exporting raw materials and the services and industrial goods produced within the cleared space contributes to overall prosperity, allows other undeveloped states to have their own improvements and, through trade, creates relations of interdependency which bring countries closer together and contribute to global peace.