When you do parallel you have a lot of wires, a lot of traces, and synchronicity issues as speed increase. You have to make sure that all of the data bits arrive as a group, this is easy to do when traveling slowly but gets very difficult as the spacing between successive messages gets decreased. Serial has a pair of wires for differential transmit and a pair for differential receive, there is no waiting or synchronization involved, you don't have mixed up messages you can just ram them down the pipe as fast as you want and you know it will be received in the right order at the far end.
In the end SATA was able to increase in speed with limited engineering effort while the layout of PATA would have required a lot of work on the synchronicity for each speed boost.
The fastest technologies tend to be a combination of serial and parallel decisions, PCI-e is a collection of serial links that run in parallel, so each one can ram data down its pipe as fast as possible and multiples get used to boost the bandwidth, but since they are all carrying different bytes they don't have to be synchronized unlike PATA with its 16 wires each carrying a different bit in the 16 bit word.