All but one are correct . #1 is considered wrong and I wonder why. As far as I know the youth has the same meaning as the young or the former cannot be used in this context?
...today show less respect for their elders than their parents did.
1. The youth
2. The young
3. Young people
'young' essentially means having lived or existed for only a short time.
'youth ' refers to the period between childhood and adult age.
The sentence is commenting on the attitude of this group of people - the youth of today: those who are not adults and their attitude toward those who are mature adults.