Islam wants us to build a duty-conscious rather than a rights-conscious society. There is a Hadith of the Prophet that says:

A believer should be duty-conscious, and as far as his rights are concerned, he should ask for them from God. (Sahih al-Bukhari, Hadith No. 7052)

A believer must give others what is due to him; as far as his rights are concerned, he should ask for them only from God. Therefore, instead of being rights-conscious, one should be duty-conscious. Another aspect to consider is that one person's duty is another's right. So, if we all follow duty-conscious principles, our rights will automatically be taken care of. Nevertheless, complete justice and total fairness are impossible in this imperfect world. God has promised that only in the Hereafter will He give every person every atom's worth of what is due to him. Thus, we must continue to do our duty faithfully seeking God's pleasure and should demand our rights in this world only from God.