A common question at this time of year is whether or not deliberately violating the law of abstinence is a mortal sin. It is. The relevant law is found in Paul VI’s 1966 apostolic constitution Paenitemini, which provides that:
The time of Lent preserves its penitential character. The days of penitence to be observed under obligation through-out the Church are all Fridays and Ash Wednesday, that is to say the first days of "Grande Quaresima" (Great Lent), according to the diversity of the rite. Their substantial observance binds gravely [Norm II §1, emphasis added].
That the keeping of abstinence (and fast on Ash Wednesday and Good Friday) is part of the substantial observance of these days is evident from the fact that the second half of Norm II names this as the chief requirement of observing these days:
Apart from the faculties referred to in VI and VIII regarding the manner of fulfilling the precept of penitence on such days, abstinence is to be observed on every Friday which does not fall on a day of obligation, while abstinence and fast are to be observed on Ash Wednesday or, according to local practice, on the first day of ‘Great Lent’ and on Good Friday [Norm II §2, emphasis added].
The faculties mentioned "regarding the manner of fulfilling the precept of penitence on such days" have to do with the ability of pastors to dispense the faithful from the obligation of abstinence and fast or commuting it to something else. If such dispensation or commutation is not obtained then "the manner of fulfilling the precept" is abstinence.
Thus one must substantially observe the law of abstinence on such days, and the obligation to do so is a grave one, meaning that it satisfies the condition of grave matter required for mortal sin. If one knowingly and deliberately fails in this obligation then one has committed mortal sin.
As to the reason for this, the Code of Canon Law notes that:
The divine law binds all the Christian faithful to do penance each in his or her own way. In order for all to be united among themselves by some common observance of penance, however, penitential days are prescribed on which the Christian faithful devote themselves in a special way to prayer, perform works of piety and charity, and deny themselves by fulfilling their own obligations more faithfully and especially by observing fast and abstinence, according to the norm of the following canons [Can. 1249, emphasis added].
It is thus a matter of divine law that the faithful are to do penance (a fact we could have determined from Scripture), and the regulations regarding fast and abstinence are simply the Church’s specification of this divine requirement, made in keeping with Jesus giving the church the power to bind and loose (Matt. 16:18, 18:18).