What did Jesus mean when He said, "enter in to the narrow gate; for wide is the gate and broad is the way that leads to destruction"?

Let's examine the text to which you refer.
Enter by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and there are many who go in by it. Because narrow is the gate and difficult is the way which leads to life, and there are few who find it.
(Matt. 7:13-14 NKJ)
Verse fourteen indicates that Jesus is talking about obtaining life. He is referring to eternal or everlasting life. The word gate refers to a door or an entrance. Jesus says that there is a narrow door or entrance that leads to everlasting life.

This specific gate is also mentioned in the Gospel of John.
I am the door. If anyone enters by Me, he will be saved, and will go in and out and find pasture. The thief does not come except to steal, and to kill, and to destroy. I have come that they may have life, and that they may have it more abundantly.
(John 10:9-10 NKJ)
Jesus is the door or gate through which we must enter in order to find everlasting life. We're saved by accepting Him as our Savior.

Notice how Jesus said the same thing in the following verse: "Jesus said to him, 'I am the way, the truth, and the life. No one comes to the Father except through Me'" (John 14:6 NKJ).

The only way to Heaven is through Jesus. The wide gate would be every belief and religion that excludes Jesus as the Savior. He's as close as the mention of His name (Rom. 10:8-13).

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