This is because the wave on the guiding structure has to match the phase of the radiated wave (the humps and dips of the sine wave have to match). A fast wave has a wavelength longer than a wave in free space, so there is an angle for the wave in free space at which the phase of the guided wave is the same as the phase of the radiated wave. For example, if the guided wave has infinite wavelength then this is a match for a wave radiated at 90 degrees (normal to the surface). For shorter guided wavelengths the wave goes off further from normal, until when the guided wavelength is the same as the free space wavelength the radiated wave is parallel to the guided wave. For shorter wavelengths than this (slow waves) there is no direction where the phases match, and radiation can happen when there are discontinuities, such as slots or probes, perhaps every 2 wavelengths, so that the phase at those discontinuities can again match the phase of the radiated wave, ignoring the changes inbetween.
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