They fit tightly to keep them from blowing off under high pressure (100+ psi).
Get good quality tire levers; I use the wide ones from Pedros. Ask the wrenches at your LBS what they use; odds are it's something they sell.
Sounds like this is a new bike; if the tires are folding they will be harder to remove than wire-beads, but will get a little easier over time as the aramid/kevlar/whatever beads stretch a bit.
Stop riding through the glass.
__________________
Today, I believe my jurisdiction ends here...