To appear offline on Instagram, you need to turn off the "Active Status" feature. This hides your online or last active time from others. You can do this from both the Instagram app on mobile and the web version.

How to Appear Offline on Instagram (Mobile App)

1. Open the Instagram app and go to your profile.
2. Tap the "three-line" menu (hamburger icon) in the top right.
3. Select Settings and privacy.
4. Scroll down to Messages and story replies.
5. Tap Show activity status.
6. Toggle off the Show activity status option to appear offline.

How to Appear Offline on Instagram (Web)

1. Go to www.instagram.com and log in.
2. Click on More from the left sidebar menu.
3. Go to Settings.
4. Scroll down and select Messages and story replies.
5. Find the Show activity status option and toggle it off.

Disabling this feature will hide your current activity status or last active time from your followers and contacts. Note that when you turn off your activity status, you won't be able to see the activity status of others either.