Why is saying Vespers on Holy Thursday and Good Friday discouraged? According to my copy of ''The Divine Office'' (the UK/Australia edition of the Liturgy of the Hours/Roman Breviary), on Holy Thursday and Good Friday the saying of Vespers is discouraged:


  Evening Prayer is said only by those who do not attend the Evening Mass of the Lord's Supper.
  Evening Prayer is said only by those who do not attend the Afternoon Liturgical Action of the Passion.


I don't understand why these offices are removed: can anyone explain it?

(The other omissions – compline on Easter Eve and the office of readings on Easter Day – are easier to understand: the Easter Vigil renders them unnecessary.)
The first thought that crossed my mind was that the obligation (at least today) of reciting the Divine Office (including Vespers) was limited to the clergy and Religious. The obligation of reciting Vespers on Holy Thursday and Good Friday has been dispensed with in our day in order to make the burden of fasting and long hours of liturgical prayer less burdensome.

Please keep in mind that there are still many religious communities and individuals who at least try to follow the older practice of fasting for 40 days during Lent.

"This ancient practice is reflected in the rubric of the Breviary of St. Pius V that Vespers are to be said before the principal meal of the day. (By the sixteenth century, the discipline of the ancient Lenten fast had been considerably relaxed, and the custom had become almost universal of anticipating all of the hours, including Vespers, to the morning, and breaking the fast around noon.)
This is also the reason why the Mass of the very last day of Lent, Holy Saturday, traditionally ends with Vespers, which return thereafter to being sung at their normal time. In some rites, such as that of the Premonstratensian Order, this custom was extended to the other days of the Triduum, and Vespers were said as the Postcommunion of the Masses of the Lord’s Supper, and of the Presanctified.

On Holy Thursday, there were originally three Masses, one for the consecration of the Holy Oils, one for the reconciliation of those who had been doing public penance during Lent, and the evening Mass in commemoration of the Lord’s Supper. All three of these Masses were normally to be celebrated by the bishop, to whose office all three of these events especially pertain. As one might imagine, the celebration of three Masses in one day was found to be fairly burdensome."- Compendium of the 1955 Holy Week Revisions Of Pius XII

The liturgical hour for the Mass of the Last Supper was restored to its' proper liturgical hour in 1930 to that of Terce (hora tertia).

The same thing happened with time for the Good Friday commemoration. Instead of being commemorated in the morning, it also got moved to a more befitting time of Terce or sometime after 3:00 PM.

If priests and Religious were to be obliged to recite Vespers after these liturgical functions it would a great burden on them physically because the Lenten fast would not be broken until after the recitation of Vespers! 

The rules for fasting have since been revised also.