On this verse, Rashi comments the following below -
אמר אל הכהנים SAY UNTO THE PRIESTS [… AND THOU SHALT SAY UNTO THEM] — “Say" and again “thou shalt say unto them" — this repetition is intended to admonish the adults about their children also — that they should teach them to avoid defilement (Yevamot 114a).
On this above teaching, its possible to learn, through implied wisdom an insight regarding the below teaching from the sages of Israel -
יוֹרֵשׁ כַּרְעֵיהּ דַּאֲבוּהּ הוּא
A son is like his fathers legs
Certainly we have a question, in what way is a son like his fathers leg? Isn't a child before a parent considered like the apple of their eye? Why leg?
And I said with the help of Heaven that the importance of a human is not just dependent on his/her level that he/she personally finds themselves on, rather it is also dependent on his/her sons and the members of their household. If they are seed that has been blessed by HaShem, and they act in accordance, and go in the ways of the Torah and being conscious in all their ways and undertakings, then even if the father/mother is not on a high level, and just based on the persons standing in society, the children may not have been held at any high regard, however, if this person is worthy to establish generations of righteousness, then by means of this, this person becomes of importance and honor follows him/her that increases.
As we can see from the Medrash -
אמר דוד לפני הקב"ה רבש"ע עני במה יקרא שמו לפניך.. על שם בנו הא כיצד אם עומד בנו בבית הכנסת ובבהמ"ד וקורא בתורה ואומרים הבריות בן מי זה אומר בן איש פלוני עני הוא ונמצאו הרבים מברכים שמו הגדול על ידו..
King David said before the Holy One Blessed Be He - "Master of the Universe, a poor man, what shall his name be called before you?" Hashem answered "On the name of his son" An example of this, if his son is standing in the house of Torah study and prayer, and gets called to the Torah, the congregation will ask him who are you the son of? And he will respond I am the son of so and so the poor man, and then we see that the masses end up blessing the name of this man via his son getting called up.
And in the same light, its the opposite for someone who has a child who does not act in accordance, G-D forbid, then even if the mother/father are righteous and scholars and of importance, none the less, that lacking will effect them as well. And the actions of the children blemish the importance and greatness they are viewed at in the eyes of humanity, who say look at this child they raised.
And based on this, there is to say that this is hinted to in the words of our sages when they said a son is like the legs of a father. As the physical size of a man depends on his legs. If he has very long legs, he is a tall man, and who has short legs is considered small. And our sages of Blessed Memory wanted to hint to us in this light, it is the same with a humans worth, that their offspring is their legs. Their children act as a measuring rod for them, that if a person is worthy to establish righteous generations, then by means of this, he/she becomes of value and honor and greatness follow him/her. And when the children don't act in a proper manner, G-D forbid, then this lacking effects the parents as well in regards to their honor and status amongst humanity.
And with this its possible to explain the words of Rashi when he says to warn to elders regarding the young, it can mean that if a parent wants to be and elder (same Hebrew word as great (Gedolim)) and on a great level, then on the young (Ketanim), then they must realize to get there, its on the young to achieve that. This means to say that if someone hustles to educate their children in the path of the righteous and guard the ways of the straight, then so too the parents become worthy to become great and important.