What phenomena show that not only attractive forces but also repulsive forces exist between molecules?

The most striking example is Brownian motion.
If we assume that there is no mutual repulsion, then tearing the paper would be as difficult as metal reinforcement. Moreover, it would be impossible to do anything with such an object. It would simply shrink to an unimaginably small size, while its weight increased millions of times.
Another example is diffusion. If there is no mutual repulsion, we will not be able to smell, even the strongest.