Why cant I see my text messages on I cloud

The iMessage app runs on a strict encrypted server that is only accessible through an apple device. Although they are stored in the cloud. For your privacy, they are only viewable through a device that is signed in with your Apple ID

Below is the description apple provides for the reasoning. I've also attached the link to the detailed information so you can read more into this.

Here's how it works

Messages in iCloud are updated automatically, so you always have the same view everywhere you use iMessage. When you delete a message, photo, or conversation on one device, it’s removed from all of your devices. And since all of your attachments are stored in iCloud, you can save space on your device.

You can use Messages in iCloud on your iPhone, iPad, iPod touch, Apple Watch, and Mac. For your privacy, Messages in iCloud is end-to-end encrypted,* which means you can't view or access Messages online via browser. 

https://support.apple.com/en-us/HT208532