'Either the people of the third world should be forcibly sterilized or the world population will explode and we will all die. We certainly do not want to die, so we should forcibly sterilize the people of the third world.' Which logical fallacy is committed in the above statement?

The argument commits the false dichotomy fallacy.

It presents only two courses: forced sterilisation or a fatal population explosion.

In reality many other paths, such as voluntary family planning, are available.

By hiding these alternatives it forces a choice between two extremes.

Rejecting the dreaded course is then made to compel the other.

Reducing a range of possibilities to just two is the false dichotomy.