Hello chalei,
Thanks for asking the Apple Support Communities for help with changing your Apple Music subscription.
Is it possible you are using some sort of a pop-up blocker that is closing or blocking the window from opening? If you are using such software, allow it for the website, or disable it and restart your device. Then try again.
Are you able to verify this in Settings?
"In Settings on your iPhone, iPad, or iPod touch
- Go to Settings > [your name], then tap Subscriptions.
- Tap Apple Music Membership.
- Tap Verify your student status. You'll be redirected to the UNiDAYS website.
- Follow the prompts to verify your eligibility. If the verification is successful, you'll automatically return to Apple Music and continue your Apple Music student subscription."
If you still have issues, it's possible the issue is cause by the network you are connected to. Try while connected to a different wireless network. You can also try by turning off Wi-Fi and testing only with your cellular connection (if possible.)
To try with another wireless network, make sure it meets these requirements: Recommended settings for Wi-Fi routers and access points - Apple Support
To turn Wi-Fi off and use your cellular connection, go to Settings > Wi-Fi, and turn the slider off. Be aware that this will use your cellular data until you turn Wi-Fi back on. (iOS with cellular data only)
Thanks and have a wonderful day.