One of the many universally agreed-upon characteristics of God is that He is omniscient, which means that he knows literally everything, and this extends to past, present, and future. He even knows all the 'what ifs' of your life. He has foreknowledge, but His foreknowledge never violates our free-will. We are not predestined in the sense that we lack the ability to choose. God has foreknowledge of our decisions, and therefore those decisions contribute toward God's plan.
To deny the concept of Eternal Security, it would appear, is to deny God's omniscience. From God's perspective, he knows every decision we will ever make, sinful or otherwise. If there was ever to be a circumstance in a believer's life where he/she would surpass some threshold of sin or even deny Christ altogether, God knew it even as Christ hung on the cross. With this in mind, how could a perfectly Just and Holy God grant this person salvation to begin with? Why would He, when He knows that this believer is going to sin or even renounce their faith in the future and thus lose their salvation? To say that He wouldn't, and that this person isn't really saved (in spite of having placed their trust in Jesus Christ) is to deny, then, all the verses which promise eternal life on the condition of faith in Christ. God knows that a believer is going to fail in the future, he knows the time, the date, the circumstances. That God is omniscient is an absolute and is one of the most elementary Biblical truths, but denying eternal security requires an implicit denial of God's omniscience, or the denial of the promises of eternal life.
The following verses all promise eternal life or salvation conditioned on faith in Christ: John 3:15, John 3:16, John 3:18, John 3:36, John 5:24, John 11:25, John 20:31, John 1:12, John 6:29, Acts 13:39, Rom 10:9, Rom 3:22, 1Cor 1:21, 1John 5:13, Acts 16:31