My textbook states that when the diffraction gap is smaller, there is more spreading of the waves. However, it seems unintuitive to me, since why would waves spread less if there is more space for it to spread?
Is there an intuitive way of understanding it?
This answer says pretty much what Quillo said in the comment. Slightly more formally, we have Huygens's principle: Each point on a wavefront behaves like a point source of waves in its own right, travelling in all 'forward' directions. So when a wavefront (of whatever shape) reaches a barrier with a narrow gap in it, the gap allows through only a piece of wavefront which is small enough to be treated as point-like, so the wavefronts that pass through are hemispherical, or, for a slit, hemi-cylindrical.
For wider slits, Huygens's principle is still applicable, but there are many Huygens point sources across the gap, and if the gap width is larger than the wavelength, light from the various points will, in general, reach points ahead of the slit with significant phase differences, sometimes (depending on angle from the normal or straight-through direction) giving rise to destructive interference; hence the patterns of rings or bands.
At this point, I recommend that you look at a textbook treatment of the simplest case: Fraunhofer diffraction at a single slit.
In addition to the argument using Huygens' principle, there is an argument based on the uncertainty principle. Short version: a small slit produces a large distribution of transverse wave vector components and hence a large distribution of propagation direction.
We have a beam of light incident on a slit. A good model for this is a plane wave incident on a slit at normal incident angle. A plane wave is only a model because it has nothing constraining it perpendicular to the direction of travel. It's infinite in extent, which is why it's only a model of the radiation field. The wave vector is directed toward the slit. There is no component perpendicular (transverse) to the normal direction.
The slit changes things. The field is now constrained in the transverse direction. It's not a plane wave anymore. The uncertainty principle tells us that the extent of a property is inversely proportional to the extent of the conjugate property. A common example is a signal varying in time, such as a radio wave pulse. A short pulse means a larger extent of frequencies, and a long pulse means a narrow range of frequencies.
In our case, the slit constrains the transverse spatial extent of the field. This is the analogue of the pulse width of the radio wave. The conjugate is the transverse propagation vector, the analogue of frequency. (The units of the wavevector are inverse meters as the units of frequency are inverse seconds.) In analogy to the time/frequency situation, a small slit (transverse extent) means a large distribution of transverse wave vectors, and a large slit means a small distribution of transverse wave vector. A large distribution of transverse wave vector means a large distribution of wave vector angle, and Bob's your uncle.
The next question will be: what is the physical mechanism at the slit for the change in transverse wave vector? The short version: scattering at the edges of the slit. Not an easy problem to solve. But midway between scattering theory and the relative simplicity of the wave vector description is Huygens' principle, which takes us back to where we started.
