Why would the water not flow out of a frostfree water bib, when you open the bib in the spring?

A frost free bib has its seal about 12" inside the visible cock. Freqquently the seal is not much more than a washer held onto a stem with a screw, others have a small cartridge-like assembly, both can come unscrewed. Some even have O rings. Shut off your main, open some faucets to blow off pressure and remove the stem from outside the house. There are many types of frost proof sill cocks Find Frostproof Faucets and other Valves at Aubuchon Hardware

It is possible that the hose bibb froze and burst over the winter, so when you turn the water on in the spring, all the water would be running inside instead of outside(hope this isn't the case, because if it is you will need to replace the complete hose bibb.).

Do you get any water out of the bibb at all?

I have never had a frost proof bib burst unless a person left a hose attached all winter. In that case everything is dry until you try the faucet in the spring, you get water inside and outside. I am picturing his cartridge came unscrewed, fairly certain

Ive seen hose bibbs burst without hosed attached due to incorrect slope of bibb. Weird thing is, they lasted for years with incorrect slope, then all of a sudden after a hard winter, they split. But I do agree that you will get water both outside and inside with split bibb. If you get water outside, but its not very strong, put your finger over the outlet, and if you can easily stop the flow of water with your finger, your bibb is split.(this just happened to me this year at my house, bibb has been fine for the ten years I've lived hear, and I always take my hoses off after use, even in the summer, its just this plumbers habit.) Then all of a sudden I went to use the bibb and low and behold I got to clean up a nice amount of water in my basement.

Mansfield sillcocks have a spring in them that sometimes gets bound or froze up over a period of non use. Shutoff the water, remove the stem and spray the spring with wd40.