May be a glitch? I’m strictly on Mobile and it allowed me to make a center.

The biggest tip I can give you is that mobile is intended for players to access Howrse when traveling or otherwise away from the computer. In reality, this game is meant to be played on a PC or laptop in classic mode, there are many things missing or otherwise faulty on the mobile app. I couldn't imagine all the wonky things you come across while using it. If you have access to a PC, I would strongly recommend utilizing it, and you'll see a huge difference in the navigability of the game.

That's just my two cents, though. I hope you figure this issue out!

this game was never meant to be an app. it was created long before apps were a thing. so things on the app don't work like the regular game. it's a lot better than it used to be

My advice is to go to the browser version on your phone. It's what worked for me to make the center when I got stuck

The mobile version does experience an error where it's unable to create the Equestrian Centre for the first time. The link it provides to the Classic version also won't work.
You'll have to go into your Account (option in the top right corner), then hit "Go to Classic Version", which will open the desktop version of the game on your phone's browser. You can use that to go through the Centre creation tutorial, and then afterwards switch back to mobile to continue playing. (You'll have to zoom in on the classic version on your phone to see it properly.) Otherwise, you can also use a computer's browser to access Howrse and complete the tutorial through there.

For future reference, there are two other beginner objectives that are difficult or impossible to complete on the mobile version. For these, you may find it beneficial to briefly switch to Classic, even if on your phone's browser.
-There's a beginner objective to "visit the Special Horses page", which is very convoluted to do on mobile.
-There's an objective to "modify your presentation" which can only be done on Classic, as presentations aren't visible on mobile.

You can flip to the classic view on your phone or whatever. It is kind of difficult to use and annoying but it can be done. I do it a fair bit for random reasons.