It is important not to confuse geographical south of Tenerife with climatic south!
At the end what really matters is the weather! Some people prefer sunny and dry South, other less sunny, but much greener North of Tenerife.
Here is the climatic map of the island – in fact it is map of rainfalls. The red-orange colour represents what people refer to as South Tenerife (sometimes without knowing this). Also you have to take in account, that apx. every 100 meters from coastline temperature drops by 1ºC, as you climb the mountain.
As you can see there are some Southern climate spots in the geographical north of the island! For example, Santa Cruz and Igueste, being almost north-most part of Tenerife, actually have spring-summer weather year-round.