Be afraid of Allah, and be just to your children
I heard An-Nu`man bin Bashir on the pulpit saying, "My father gave me a gift but `Amra bint Rawaha (my mother) said that she would not agree to it unless he made Allah's Messenger ( may the peace and blessings of Allah be upon him ) as a witness to it. So, my father went to Allah's Messenger ( may the peace and blessings of Allah be upon him ) and said, 'I have given a gift to my son, but `Amra bint Rawaha asked me to make you as a witness to it, O Allah's Messenger!' Allah's Messenger (may the peace and blessings of Allah be upon him ) asked, 'Have you given (the like of it) to everyone of your sons?' He replied in the negative. Allah's Messenger (may the peace and blessings of Allah be upon him) said, 'Be afraid of Allah, and be just to your children.' My father then returned and took back his gift."
In brief, giving the children equally is a must if one fears of harming one of the children or that his giving may cause severing the ties of kinship, which is often expected.
If giving the children equally is obligatory, the father must not distinguish one of them except with their permission and consent.
This Hadith in its various wordings necessitates giving the children equally, unless there is a Sharia approved reason that calls for distinguishing one of the children, as the necessities render permissible the prohibited matters as it is known from the Qur'an and the Sunnah.
Just as giving the children equally is required in Islam, treating them equally - as much as possible – is required so as not to cause them to hate each other.
Any preference for one of the children leads to the hatred between the children, they would grow up on separated and hating each other, parents certainly do not agree with such hatred despite the fact that they caused it.
Parents are required to instill love and mutual understanding between their children through the best educational methods, the most important of which is treating them equally as much as possible.
Dear parents be mindful of the fact that you will be held accountable before Allah, so let your children grow up according to the instructions of Islam.