Why would it make it harder for young people to get employed if the wage was $10?
The key benefit to the young is that, whilst they are inexperienced, they are typically cheap - that's why they tend to do unskilled jobs or the most junior positions in skilled areas. As they get older, gain experience and skills, they get paid more.
If you force companies to pay more for the same quality of labour, the benefits to hiring these younger people goes down. Someone else has mentioned it, but if you have a job opening that pays $8 an hour, and you have one potential employee expecting $8/hr and another, slightly better and more experienced candidate that expects $10 an hour, you have to decide - is that extra experience worth the extra cost? If it's an unskilled job, you'll possibly decide that it is not. If the minimum wage goes up to $10 an hour, then of course you'll take candidate number two - if you're paying them the same anyway, you'll always go for the better candidate. The problem here is that the young - those who have just graduated school or college and who have little experience - then find themselves in a situation where they are potential priced out of the market; Not because their labour is worthless, but because there are other, more experienced candidates available at the same price.
As a real life example, the UK didn't have a minimum wage before 1997. It was introduced and employment continued to rise (we were in the middle of a large boom, of course) for all demographics - except the young. For them, it more or less stayed stagnant - they were the only ones whose employment prospects didn't really improve in the boom. From 2005, in fact, they started to get worse.
This is the case for anyone who's unskilled, but it affects the young the most because they are the most likely to be unskilled and inexperienced.
