As @curiousdannii mentions, it's no issue that one specific word isn't used, there are plenty of others; while I don't know Greek, I'm sure there are words meaning 'torment' or 'torture' that don't appear in Scripture either.
So, to answer your question, we believe what we do because there are many passages in Scripture that indicate the wicked will be destroyed rather than living in torment forever; examples include Matthew 10:28, John 3:16 and Jude 1:7. Not only this, but we believe these passages significantly outweigh those used to defend the traditional view, both in number and strength.
Additionally, the concept of destruction/death as punishment fits what we see of God's judgment throughout the Bible; death is always the ultimate punishment, God never sentences anyone to be tortured in His commandments to my knowledge.
There are other, secondary arguments, based on the character of God and the nature of sin, but Scripture is the primary basis for most of us.