I think part of it is ratio. Classical styles tend to be very broad, and have lines that draw the eye to how wide they are. Gothic tend to be taller and have lines that draw the eye to heaven. There are other tricks as well, I'm sure, but those are the most obvious ones I've noted.
Certainly. Thinking about it, Gothic architecture has several things which make it appear less "solid" compared to classical architecture:
1) As you said, ratio. Classical buildings tend to be broad, which means they fill up the visual area, while Gothic buildings go upwards. This is important because human eyes are set horizontally, so if two buildings have same area, vertical one will leave field of vision much sooner than a horizontal one.
2) Detail. Classical styles usually also tend to have more massive ornamentation, and in general details on them are just larger. Gothic architecture employed novel building techniques to allow it to be slimmer in general - it is not just that the lines draw the eye to the heaven, but building elements themselves are more gracile. And while classical buildings tended to have a large area with ornamentation (e.g. Parthenon), in Gothic architecture the ornamentation is often inset - one ornament will surround or contain a different style of an ornament (see examples
here and
here - notice how even if you remove the window itself in the first image or the sculptures in the second, there is still extensive ornamentation remaining. Compare this to
reconstructed Partenon or
Pantheon, where main decorative elements are massive and self-contained, so if you remove them, all you have left is an empty space). Basically, you could say that Gothic architecture is, in a sense,
fractal. See
here on why this matters.
3) Orientation. When you look at the Gothic buildings, both the building itself and the ornamentation on the building - arches, sculptures, details of the wall in general, all point upwards. Ornamentation on the Greek temples tend to be read like a book - from side to side (see example
here). Sculptures on the Gothic buildings tend to be self-contained in their alcoves, and their stance and setup tend to draw the human eye upwards.
4) Utilization of light. Unlike previous building styles, Gothic architecture tends to have large windows, which again have a pointed vault. And not only windows are large, but there are several architectural elements - specifically the flying buttresses - that allow the structure to expand into the space without taking it up. Romanesque churches end where their walls end; Gothic churches do not.