Self analysis


Under the app you will need to click on "Computer" then click on Black which shows a PC icon at the moment. Once you click on it it will turn into a person icon. Now click Continue.

Under the app you will need to click on "Computer" then click on Black which shows a PC icon at the moment. Once you click on it it will turn into a person icon. Now click Continue.
The newest version of the Android app doesn't have that option, so it is possible the OP has that. It isn't available to everyone last I saw.
If it is version 4.x it doesn't have that.

I am still using version 3.8.8 and it works. So if I update I will lose that function to play against myself?!

I am still using version 3.8.8 and it works. So if I update I will lose that function to play against myself?!
Yes.

They changed the app layout
If you want you can uninstall the current and download the previous version from here...
https://www.apkmirror.com/apk/chess-com/chess-play-learn/chess-play-learn-3-8-8-release/