Why are planets not crushed by gravity?

In very simple terms which I hope you will understand.

The gravitational force of attraction depends on mass and distance.
For the atoms which make up the Earth there are two forces acting on them, the gravitational attraction due to all the other atoms and the Coulomb/electrostatic repulsive force between the electrons orbiting the atoms.
The electron shells repel one another.

As mass increases the gravitational attractive force increases and the atoms come closer together and the repulsion between the electron shells increases to balance the increased gravitational attraction.

If the mass increases even more the Coulomb repulsive force cannot balance the increased gravitational attractive force and the atom collapses with protons and electrons combining to form neutrons.
You then have an entity composed of neutrons - a neutron star.

There is still the gravitational attractive force between neutrons but now the repulsive force is provided by the strong nuclear force between the neutrons - neutrons do not like to be "squashed".

Increase the mass even more and the gravitational attractive force increases and so does the repulsive force between neutrons by the neutrons coming closer together.

Eventually if you increase the mass even more the repulsive force between the neutrons is not sufficient to balance the gravitational attractive force between the neutrons and so you get a further collapse into a black hole.

So the simple answer to your question is that the gravitational forces between the atoms which make up a planet are not large enough to initiate catastrophic collapse because the mass of a planet is not large enough.

Planets are crushed by gravity! That's why, for example, Earth is a densely packed spherical rock rather than a loose cloud of dust.

There's just not enough crushing 'force' to do more than that.

The particles which make up atoms are electrically charged, and they repel each other when they get too close to each other. Gravitational forces only attract one particle to another, and never repel, but they're extremely weak compared to the electrical force. To create a black hole, the gravitational force needs to overcome these repulsive forces between particles. For objects like the earth and the sun, the repulsive forces are much greater than the gravitational force.