The Compact Disc arrived in 1982 and was a joint development by Philips and Sony. Philips had already created a manufacturing process for a new disc based system in the shape of LaserDisc - a very high quality video format that saw little take-up apart from serious movie buffs who couldn't stand the poor image quality offered by VHS. Although LaserDisc employed analogue video, the audio could be encoded digitally, so the basis was there for an audio only disc for music. Taking video out of the equation also meant that the large 12in diameter discs that were used for the LaserDisc format, would not be needed for music alone - hence the Compact Disc was born.
As with most new technologies, early CD hardware was expensive and only available to a select few with large bank balances. Also, the cost of the discs themselves was considerably higher than traditional vinyl and cassette based formats. In order to make Compact Discs more attractive, many record companies created special versions of albums on CD, usually with extra material that wasn't available on any other format. This did convince many consumers to dig deep and invest in CD, but for the vast majority of end users, it wasn't until the hardware reached a truly affordable level that they turned their back on their old vinyl turntables.
For the most part CD was a clearly superior option to vinyl - the discs were smaller, more resilient, didn't need to be flipped over, the sound quality was arguably better and, being a non contact medium, that sound quality would not degrade over time as it would with vinyl or tape.
The invention of the Compact Disc marked the beginning of the digital revolution in the music industry, but in no way did it herald the end of the Compact Cassette. CD brought with it inherent advantages like instant track skipping, but despite the fact that Compact Discs were considerably smaller than the 12in vinyl records they replaced, they were still significantly larger than cassettes, which made them far less compelling as a mobile medium.
That's not to say that mobile, personal CD players didn't flood the market, because they did. Unsurprisingly, Sony was quick to jump on the bandwagon, launching its Discman brand. Leaving the Walkman brand behind in the digital age was a big mistake, and eventually Sony reverted to calling its personal CD players CD Walkmans in the late 90s, but the damage had been done by then.
Early personal CD players were not just large in diameter, but also thick and generally bulky, with poor battery life. Early players also suffered from severe skipping whenever the devices were shaken or bumped, making them unsuitable for anyone who wanted to go jogging while listening to music. Considering that most tape based players at this time employed anti-roll mechanisms to ensure clean playback regardless of vibration and bumps, CD based units were not popular with active users.
As the personal CD player evolved, issues like track skipping were soon addressed with digital buffers, while the players themselves became unfeasibly slim and light. But even the most wafer-thin Discman, still wouldn't fit in your pocket due to the unavoidable diameter of the disc itself.
But the biggest problem with CD as a personal stereo medium was the inability to record to the format. It wasn't until the late 90s that CD writers and the blank media that they employed became affordable, and even then you needed to have a PC and reasonable technical ability to throw your own compilations together.
None of these issues stopped the Compact Disc from making a serious impact on the personal audio market, but its inherent limitations meant that it was never going to enjoy the kind of adoption and support that the cassette based personal stereo did.