The sharpest reason the gate is narrow is this: you can miss it. You miss it if you refuse to admit that you are a sinner who needs a Savior. That is the one entrance requirement, and it is the one our proud hearts resist most.
Stand at that door and take honest inventory of what you brought. There is no magical key inside you. There is no spark of divinity waiting to be discovered. There is no résumé of religious performance that turns the lock. All you have as you stand there is your need, and you must be humble enough to say so out loud. Craig Blomberg notes that the Sermon on the Mount opens and closes on the same note: the kingdom belongs to the poor in spirit, and the gate opens to those who knock.
That is why Jesus put verses 7 and 8 just a few sentences before verse 13. The same sermon that commands you to enter tells you how the door opens. Not by your strength. Not by your obedience. Not by your faithfulness. It opens to the one who knocks. The broad gate asks nothing of you at all; the narrow gate asks only that you come with empty hands and confess that you cannot save yourself.
Hear what this is not. This is not a joyless, cramped little religion for people who love rules. This is the doorway to life. But it is a doorway, and a doorway by definition lets some things through and keeps others out. What it keeps out is the illusion that you were ever going to manage this on your own.