the latches are on the sides of the box door, the center does not have any moving clasp, just the 2 sides about 1/4 of the way down from the top. I say you got something either stuck in side A, B or center . Its obviously not locked.(I hope) These gloveboxes arent very roomy, so it makes sense to have something jam it up. Under the glovebox is a leg airbag...there are philips head screws that should allow further access - you should be able to access the glovebox from there - just be careful around airbag components.
Depending on where it sticks, one of those plastic trim tool mini pry bars might help. I don't remember if removing the shiny black trim piece under the door provides additional access to hinges or not. It's easy to remove if you want to look, pry straight out from dash using the mini pry bars. If you don't have a set of trim tools, stop by Harbor Freight as may be best under $10 tools you can buy.