How do I log into iCloud from my iPhone or iPad?
iCloud.com behaves this way because you should, theoretically, be able to do everything you need to elsewhere on your device. If you find yourself in a situation where you need to get into your iCloud account through the web, you can still do it by tapping the share button and tapping "Request Desktop Site." This will get you there but it won't be pretty as it isn't optimized for mobile.