It is difficult to justify deforestation for any reason, given the essential role forests play in sustaining life on Earth.
There are many reasons for hunger, but the existence of forested regions is not one of them. Especially in the era of industrial farming, which certainly entails risks to the environment when left unregulated, the problem of hunger is not one of scarcity but of distribution and integrity as well as control of conflict. Americans throw away enough food every day to feed entire cities on a regular basis. Additionally, much foreign assistance provided in the form of processed foods is subject to local corruption and to limitations in recipient country infrastructures (in effect, getting food from dock to those in need can be extremely problematic if roads and/or rail networks are inadequate). Millions of the world's hungry are in that state due to ongoing wars that cause mass migrations and that destroy farms and factories.
Forests and jungles are vital to the production of oxygen, without which live on Earth would cease to exist. Deforestation reduces the ability of the planet’s natural ecosystem to replenish itself at rates commensurate with population growth. Furthermore, deforestation creates enormous problems in regions like South Asia (especially Bangladesh) and Southeast Asia (e.g., Indonesia). Heavy rains that might otherwise have been contained by natural vegetative growth are allowed, following deforestation, to wash away everything in the water’s path, including villages and farmland.
In short, deforestation is not at all a response to hunger; in fact, it exacerbates the problem by creating conditions unsuitable for agricultural production. So-called “slash and burn” farming techniques, especially in the Amazon, may provide for food production in the short term, but in the long term, those fields invariably fail due to improper agricultural practices while the environmental problems associated with deforestation increase.