Matter is almost entirely empty space
Chown points out that atoms, despite feeling solid to the touch, are overwhelmingly empty: the nucleus occupies a minuscule fraction of an atom's total volume, with the rest occupied by electrons whose exact positions are only ever described probabilistically. The sensation of solidity we experience when touching an object comes not from atoms packed tightly together but from electromagnetic repulsion between the electron clouds of adjacent atoms refusing to overlap.
This means that if all the empty space were somehow removed from every atom in your body, what remained would be unimaginably smaller than you'd expect — a fact that has nothing to do with objects being fragile or insubstantial, since the forces holding that mostly-empty structure together are extremely strong.
Takeaway: solidity, as we experience it, is a story told by forces acting across empty space, not a story about densely packed matter.