I'm a girl 21years old. There is a man in my life that I love very much. He loves me too and wants to marry me. He asked my hand of my father and he agreed, but his family don't love me because there is another person of his family that asked me to marry him. I refused because I love this man! Am I right or not?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If the young man you mentioned is of good character and if he is pious, then you are right in what you did. But if he is not so, then what you did is wrong and you should wait for the pious good young man.
As for the opposition of this man's family it is to be considered mainly if his parents are among the people who are against this marriage. If that is the case, he should deal with them patiently and kindly, trying to convince them and if necessary he could seek the help of other people in this respect. As for the other people opposing such an act, he can deal with them kindly and so can you.
But do not forget to ask Allah to give the best for you. We ask Allah to ease the matters of us all.
Allah knows best.