The guys & gals making thin wallets will skive all the edges of the card pockets & the edges of the main body of the wallet to achieve a thin wallet.
Certain card pockets shapes also help with keeping the wallet thin.
I started out with a leather kit from Amazon. It was like $140 & had all the basic tools to get started.
Plus it had 4 colors of thread, beeswax plus some other stuff.
I made a lot of stuff with that kit.
4 inch Square double layer coasters. Tool 1 side or both sides. Teach them stitch line layout, the border layout, then the stamp pattern layout. Then glue & stitch the double sided coaster together. Can even make a leather coaster holder.
I am going say, user error. You probably moved the piece when sewing or it slipped a bit while sewing.
I am no means a professional & I've only used my class 26 maybe 6hours total.
Maybe some more experienced pros will chime in.