The point is "a" fourth dimension vs "the" fourth dimension.
Our 3D space uses all 3 dimensions interchangeably. It makes sense to talk about "the" 3 dimensions of space.
If you look at 3D + time, time acts differently than the other 3D.
- we only move through time in 1 direction, at a rate of pretty much 1 second per second.
- things break more easily than they go back together (ex. shattering a glass)
So time doesn't fit in with the other dimensions. Or does it? Einstein crammed it in there, and proved that time would be the same except we're being constantly pulled in the timewards direction by a really heavy object that we can't see. Or something like that.