May cast spells are usually triggered by some move you make, or some move the opponent makes. Triggers can vary place to place, and are not a guarantee its gonna work.
The now famous "healing tweak" done to the pets now have me thinking the "may cast" spells are kind of useless. When you need it, the pet wont, every time. Solid stats however, are not subject to 'tweaking' in this manner, and are more stable. Aka something you can depend on.
If you have something that says it does something, and doesn't? If i have a pen, and it runs out of ink, I don't write with it. Same idea. Try to hatch and get more reliable stats.