The Earth has a finite amount of natural resources, and anything finite will eventually run out. The excess trash will increase pollution to the soil, water and air eventually making it near impossible to inhabit the planet. Most of the other species that inhabit the Earth will become extinct.
Humans consume natural resources at an alarming rate, and the Earth takes decades or even centuries to reproduce them, so the balance is already largely offset. Space designated for landfills are also finite, so when recyclable materials are thrown away, it adds to the amount of trash piling up; this will in turn create even more landfills and encroach on the space that we live in and the habitat of other species.
Many recyclable materials that are either thrown into landfills or other environments harm the Earth; plastic for example breaks down into smaller fragments over time, those fragments then start to absorb toxins that pollute the water and soil, in some cases it can make animals sick. Other materials, if not recycled, can cause just as much damage. The natural Eco system has a delicate balance; therefore, causing excess pollution and invading the habit of animals, their numbers will start to rapidly reduce until they become extinct. Fertile land and clean water sources will become unusable due to pollution.