To determine the option that does not weaken the argument, we need to identify the option that does not provide a potential reason for over one hundred thousand 17 and 18-year-olds to still sign on for unemployment benefits despite the government introducing the Youth Training Program. Let's analyze the options provided:

A. The program provides uninteresting work.
This option weakens the argument by suggesting that the Youth Training Program may not offer engaging or fulfilling work, which could discourage teenagers from participating and lead them to opt for unemployment benefits instead.

B. It is difficult to find work for all the program's graduates.
This option weakens the argument by indicating that the program may not have enough job opportunities to accommodate all its graduates. If the graduates struggle to find work, they may end up signing on for unemployment benefits.

C. The number of 17 and 18-year-old youths has increased over the past three years.
This option does not weaken the argument. If the number of 17 and 18-year-olds has increased, it could contribute to the high number of teenagers signing on for unemployment benefits, as the program may not be able to accommodate all the new participants.

D. Unemployment benefits are known while future salaries are not.
This option weakens the argument by suggesting that teenagers may prefer the immediate certainty of unemployment benefits over the uncertainty of future salaries that they may receive through the Youth Training Program.

E. Youths are unaware of the program's benefits.
This option weakens the argument by suggesting that teenagers may not be aware of the benefits offered by the Youth Training Program. Their lack of awareness could lead them to choose unemployment benefits instead.

Based on the analysis, option C is the one that does not weaken the argument. The increase in the number of 17 and 18-year-olds over the past three years can be a contributing factor to the high number of teenagers signing on for unemployment benefits, regardless of the introduction of the Youth Training Program.