Why does a father refuse to solemnize the marriage (aqd al-qiran) for his engaged daughter until she finishes her studies, despite the daughter's desire to complete the contract to enjoy lawful love and avoid falling into sin?

There is no prescribed limit for engagement in Islamic law, and there is no harm in extending it to complete your studies. However, this should not be the case, and your father is not permitted to prevent you from marrying for the sake of studying. You should strive to convince your father to finalize the marriage contract (aqd al-qiran) so that you can meet your fiancé and go out with him, even if the consummation of the marriage is delayed after the contract. You should not tell your fiancé that you love him before the marriage contract, as he is a stranger to you. We advise you to strive to convince your father to expedite the marriage contract and to enlist the help of relatives for this purpose.