Adding a ceiling fan single switch in a box with 3 way switch in older house
You don't have a neutral at the switch. White is a traveler, and should be marked in some way to indicate that it is not a neutral (but is likely not marked). Red is the other traveler, and black is common (either attached to power or the light, depending on which switch it is). Multiway Switching can be confusing, and is the subject of many questions on this site.

This is likely what the circuit looks like



You're describing the wiring at switch 2, where the black wire is only "hot" when both switches are in the proper state (both up, or both down. Unless one is installed upside down). When the switches are toggled, one of the travelers between them will be energized.