private mode safari doesn't work

Hello chanhunzin,

To help resolve this issue, check and make sure there isn't any profiles installed on your iPhone that could restrict you from using private browsing. "You can see the profiles you have installed in Settings  > General > VPN & Device Management."

This article explains how to remove configuration profiles on your iPhone:

Install or remove configuration profiles on iPhone

If the issue persists, try the steps in this article to help resolve issues with the Safari app. Even though the article title is different from the issue, these steps can help:

If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open

Thanks for using the Apple Support Communities, and have a great day!

Hi chanhunzin,

We'll be glad to help you out. Generally, the option should always be there. Do you have any restrictions turned on? See the "Prevent web content" section of Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

"Prevent web content

iOS and iPadOS can automatically filter website content to limit access to adult content in Safari and other apps on your device. You can also add specific websites to an approved or blocked list, or you can limit access to only approved websites. Follow these steps:

1. Go to Settings and tap Screen Time.
2. Tap Content & Privacy Restrictions and enter your Screen Time passcode. 
3. Tap Content Restrictions, then tap Web Content.
4. Choose Unrestricted Access, Limit Adult Websites, or Allowed Websites. 

Depending on the access you allow, you might need to add information, like the website that you want to restrict."

We hope this clears things up.

Cheers.