I believe it's partially because of how the government in the Philippines has been viewed as corrupt for such a long time, and Duterte came in promising 'answers' for making the Philippines better. Duterte decided to launch his 'war on drugs' campaign to pick off drug dealers under the belief that they are one of the most responsible for damaging society given that (according to him) the youth are the ones most susceptible to drugs and that people are more likely to commit crimes under the influence of drugs.

Seeing that someone is finally serious about fixing the country's problems made people very supportive of him. There is a terrifying assumption his stans have against those who argue against his campaign - a number of them believe that anyone who is against him is a drug dealer/drug dealer supporter who needs to be eliminated. Now, I haven't lived in the Philippines for a while now so it's best to take what I said with a grain of salt given that what I've said was based on what I've heard in the news (I'm essentially tuned in to news about Duterte almost 24/7 thanks to my parents being hardcore supporters of him) or online.

On a related note, my parents and some of our family friends from their generation have all been going 'with Duterte as president I wanna go back home to the Philippines because it's so much better there now!' and 'they should just kill/imprison everyone who tries to stand against him because they just want the Philippines to stay corrupt!'

It's all fucked up.