Obligatory Wiki link to a true example of a highly viscous liquid.
If you choose to define “solid” as what a liquid becomes after passing through a first-order phase transition (complete with a latent heat of fusion), then glass is not a solid, as it doesn’t do that. If you choose to define “solid” as something exhibiting resistance to deformation, then glass is a solid.
Either definition is reasonable, hence the confusion.
Of course, it doesn’t matter much what you call it, so long as the speaker and listener know what glass actually is.
Preceded by Lord Kelvin’s pitch staircase (a pdf) in Glasgow, which was started in 1887.
The timeline table makes for riveting reading.