It is a myth. During puberty, the hair will steadily increase its growth rate and its density on your skin. This happens regardless of whether you shave it or not. The hair seems thicker after shaving because the tapered, bleached hair is cut off and what grows out of the skin to replace it is stiff, darker, and full thickness.
For men, the amount of hair can increase well into their thirties. It is not uncommon for some men to have hairless chests in their twenties and very hairy chests in their thirties.