Eternal security is the doctrine that when a person is saved nothing can affect their salvation. They can never lose it for any reason. I believe Eternal Security is true because of the following verses:
John 3:16
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
John 6:37-6:40
"All those the Father gives me will come to me, and whoever comes to me I will never drive away. For I have come down from heaven not to do my will but to do the will of him who sent me. And this is the will of him who sent me, that I shall lose none of all those he has given me, but raise them up at the last day. For my Father's will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day."
John 10:27-29
"My sheep listen to my voice; I know them, and they follow me. I give them eternal life, and they shall never perish; no one will snatch them out of my hand. My Father, who has given them to me, is greater than all; no one can snatch them out of my Father's hand."
Tell me, how can you read those verses and NOT believe in Eternal Security? Jesus is extremely clear. Out of all that the Father gives to Jesus he will lose NONE of them! In other words, Everyone's salvation is Eternally secure! It's right there in black and white! So, what do you think? Is Eternal Security real? Why or why not?
The Gospel of John verses you quote are saying no power can forcibly snatch you away from God. Notice how in that key verse 27 there is a certain characteristic of His sheep --
27 "My sheep listen to my voice; I know them, and they follow me."
See what His sheep are doing in the verse? They listen, and then they also follow. 2 actions.
A person that comes to Him at one time could walk away though... This reminds of us His parable about the seeds falling on various types of ground, some of which don't root deeply, and then wither and die. (Matthew 13:1-9)
In the Gospel of John, Christ instructs us that even if we continue to remain on the vine, that we must bear fruit or be cut off (read fully, but you will also see verse 2 and verse 6) --
1 “I am the true vine, and my Father is the gardener.
2 He cuts off every branch in me that bears no fruit, while every branch that does bear fruit he prunes so that it will be even more fruitful.
3 You are already clean because of the word I have spoken to you.
4 Remain in me, as I also remain in you. No branch can bear fruit by itself; it must remain in the vine. Neither can you bear fruit unless you remain in me.
5 “I am the vine; you are the branches.
If you remain in me and I in you, you will bear much fruit; apart from me you can do nothing.
6 If you do not remain in me, you are like a branch that is thrown away and withers; such branches are picked up, thrown into the fire and burned.
7 If you remain in me and my words remain in you, ask whatever you wish, and it will be done for you.
8 This is to my Father’s glory, that you bear much fruit, showing yourselves to be my disciples.
9 “As the Father has loved me, so have I loved you. Now remain in my love.
10 If you keep my commands, you will remain in my love, just as I have kept my Father’s commands and remain in his love.
11 I have told you this so that my joy may be in you and that your joy may be complete.
12 My command is this: Love each other as I have loved you.
13 Greater love has no one than this: to lay down one’s life for one’s friends.
14Y ou are my friends if you do what I command.
15 I no longer call you servants, because a servant does not know his master’s business. Instead, I have called you friends, for everything that I learned from my Father I have made known to you.
16 You did not choose me, but I chose you and appointed you so that you might go and bear fruit—fruit that will last—and so that whatever you ask in my name the Father will give you.
17 This is my command: Love each other."