Humility towards children
Anas (radi Allahu anhu) passed by some children and greeted them (by saying Assalamu Alaykum to them). Then he (radi Allahu anhu) said: The Prophet (sal Allahu alaihi wa sallam) used to do the same.
[Sahih Al-Bukhari and Muslim]
To greet (saying Assalamu Alaykum) small children is an excellent expression of humbleness.
Similarly, a believer is also recommended to greet his wife and children while entering his home, and this will be a sign of his humbleness as well.
The believer is also supposed to greet those who may be less in worldly status than himself (such as a servant etc.). Not doing this may be an indication of pride and arrogance and shows a deviation from the practice of the Prophet (sal Allahu alaihi wa sallam) which is enough to incur the displeasure of Allah.
And Allah knows best!