Usually a fully developed blackhead does not become inflamed until it is squeezed. When it is squeezed, the sebaceous follicle and tissue around it can be injured. This can result in an inflammatory reaction.
Squeezing a whitehead can be even more harmful. These are more likely than blackheads to become the sites of inflamed lesions. Squeezing and picking pustules can aggravate the inflammatory process. Some pimples have openings that are so small that they cannot be extruded by pressure anyway. Applying pressure to these will only result in damage to the sebaceous follicles and will worsen the inflammatory reaction.