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Does it have something to do with soft ferrite's low coercivity, still not low enough at gigahertz frequencies?

See, I'm putting together high gain receiver antennas and transmitter antennas. Space is an issue. So maybe the same as ferrite rods allowing for antenna meters and meters long to be coiled around said ferrite rod just a few inches long, ferrite rods will do it for WiFi antennas.

Am I wrong? If so, in what aspects?

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Ferrite rod antennas were historically used for broadcast AM receivers. These signals are around 1 MHz, which corresponds to a wavelength on the order of 300 meters. A half-wave dipole at this frequency would be on the order of 150 meters long. The very high permeability of ferrite allows this antenna to be made smaller, at the cost of some performance. It is a form of electrical shortening.

For Wi-Fi, the signals are around either 2400 MHz or 5000 MHz. Half-wave dipoles at these frequencies are around 62 mm or 30 mm. This is small enough that even a full size antenna is usually not inconvenient. That's why ordinary Wi-Fi gear does not use ferrite rod antennas: there's no need for them.

However, if you are making a directional antenna, an array of such antennas might be inconvenient, and you could want a way to make it smaller. In theory, could use a material with a higher magnetic permeability, such as ferrite. However, you'd have difficulty finding a suitable material. It takes some amount of energy to flip the magnetic domains in a ferromagnetic material, and this energy is lost as heat. With increasing frequency this flip happens more times per second, and thus the total power of these losses becomes higher. Losses due to this mechanism are called hysteresis losses.

Consequently, at Wi-Fi frequencies the ferrite material used for an AM antenna would make a very good heater and a horrible antenna. There are modern ferrite mixes that have lower loss at microwave frequencies, but they have lower permeability.

However, if you can load an antenna with a high permeability material, then duality would suggest it's possible to do the same with a high permittivity material.

In fact, it is. There are dielectric materials with acceptably low losses at microwave frequencies. They aren't even especially exotic or expensive. We call it plastic.

I'd give you some references, but I can't find any good, free, online canonical references. There are plenty of examples and research papers though: search "dielectric rod antenna" and "dielectric loading".

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    \$\begingroup\$ Did a typo creep into your wavelengths (should be mm instead of cm)? \$\endgroup\$ – steeldriver Jan 15 '15 at 15:16
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    \$\begingroup\$ Not only that; the ferrite core allows you to wrap several meters of wire around the core to get an N^2 amplification of the signal (where N is the number of turns). Since the frequency is so low, all that wire does not introduce much phase shift. However, for wifi you would be limited to a couple of cm, tops - not enough to get much gain at all. \$\endgroup\$ – alex.forencich Jan 15 '15 at 20:07
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Ferrite kind of gives up the ghost as a useful concentrator of magnetic flux above 100MHz. As WiFi operates 2.5GHz, ferrite isn't very useful. If you look at the highest frequency ferrite Fair-rite have to offer you'll see this graph: -

enter image description here

Notable is the permeability - only 16. Also notable is the frequency at which the resistive losses equal the permeability - about 400MHz. Above this frequency the ferrite behaves like a typical ferrite bead and suppresses signals.

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