A necessary condition is a condition which must be true in order for an event to happen. A sufficient condition is an condition which, if true, guarantees an event will happen.
By confusing necessary and sufficient conditions an argument is flawed. For example:
To buy drinks you need to be 18, Harry is 18 therefore he will buy drinks for us
Here being 18 is necessary condition which needs to be met for Harry to buy drinks. It is however not sufficient to buy drinks, Harry will need money and be thirsty (amongst many other things!). Another example:
Radiation causes cancer, Kevin has cancer, therefore he was exposed to radiation.
In this example exposure to radiation is a sufficient condition to cause cancer, that is if it is true (i.e. Kevin has been exposed to radiation) then Kevin will get cancer. The flaw in the argument is that exposure to radiation is not a necessary condition to cause cancer, it can caused by other things such as asbestos.
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