I'm not an expert in this field, but I suspect it has something to do with the light receptors in the eye. To explain, we have three different types of color receptors (cones) in the eye. They each respond maximally to a certain wavelength of light (blue is optimal for one type of cone, green for another, and red for another - these cones can be called by their maximally responsive color; "blue", "green", "red"). Importantly, these cones also respond to other, non-optimal light frequencies. Therefore, the color we perceive is the blending of each of their responses. Violet light causes a large response in the "blue" receptors and a small response in the "green" and "red" receptors. While, red light causes a large response in both the "red" and "green" receptors, but a minimal response in the "blue" receptors. Thus, it could be that the response combination of the three different receptors on the violet end of the spectrum ends up being similar to the response combination of the three different receptors on the red end of the spectrum. By being similar, I mean that our perception is similar even though we have two different mixes of responses from our receptors. This would be like being able to take two different roads to end up at the same place (in this case, a similar color). Therefore, the visible light spectrum appears to be continuous when we make it into a wheel.