What makes an epoxide stable?
Well, you have to ask: how stable? and compared to what?

Epoxides, including ethylene oxide, are generally considered relatively unstable molecules, with a high chemical activity and involvement in numerous reactions, including polymerization and thermal decomposition. However, ethylene oxide does exist as a molecule, as does cyclopropane, which also contains a three-membered ring.

So, let's compare for example the ring strain in ethylene oxide and cyclopropane. I found some computation data on their relative stability from these lecture notes, which indicate that “ethylene oxide has less ring strain than cyclopropane”. I would attribute this to the fact that the C–O–C angle has less strain because its “relaxed” value would be 104.5°, compared to the “relaxed” C–C–C angle of 109.4°.