why are chain letters illegal ?

The reasons hinges on mathmatics. Suppose the letter says --

". . and send a letter to 12 friends or else . ."

that means that the number of letters sent will be . . .

12 - by the first person

144 - by the people who get the "first person's" letter

1,728 - by the people who get the "second 'person's" letter

then 21,000 letters are sent -

then 0.25 million -

then 3 million -

then 36 million -

then 430 million -

then 5.2 billion

so - - - since all participants do not have an equal chance of "winning" -- it is illegal