A big dog could break osb board like that, especially if it's old and wet.
My clean out and chicken door was originally osb board but I swapped them out for 3/4" plywood.
I was able to get my fingers under the door and pry it 2" without much resistance. 
 
Around here, osb is about 1/4 the price of plywood so if you're determined to still use osb, add another latch.
In your image, you have one central latch.  Add another latch 1-2' off the ground.  Might help to stop the bottom of the door from being opened so easily.
 
Another thing you could try is to trim out the door with some 2x4 (2x3 would work too), on the sides and top, leaving 1/4" clearance for the door.
I do this personally, not for prying fingers, but to stop the rain from running down behind the door.  If an animal can't get behind the door, they can't pry it.