Why dont most parasites kill their hosts immediately

They have evolved not to, and they don't want to look for a new host.

Explanation:

Many parasites have evolved to take from their host a small amount. Over time, it does add up, but parasites try not to kill their hosts. If they do, they will need to find a new host.

Parasites don't kill their host because they depend on the host for survival. They rely on the host body activities like digestion, circulation, respiration to be able to grow, multiply and survive. Without the host, they cannot survive.

Explanation:

Parasites are organisms that live on or in another organism (host) there by feeding on the organisms nutrients and body and causing infections or damage to the host organisms.

Parasites depend totally on their host for survival. They depend on the host body function to live, multiply, grow and even benefit from their host immune system.