Why veil the statues in the Holy week and no Mass on Good Friday?

As you can see the statues in the Church are veiled during Holy week. It is not mandatory since the Vat.II, and so not all Churches do that any more. The rational behind this practice is that:

Christ hid himself from the rage of the Jewish authorities (John 8:59), as they threatened to stone him;  so now he is hidden from the world in preparation for the mysteries of his passion.

“The statues of the saints, too, are covered; for it is but just that, if the glory of the Master be eclipsed, the servant should not appear.

Another reason is that  our Savior’s divinity was almost totally eclipsed during the holy week, so great was his suffering. And even his humanity was obscured – so much so that he could say through his prophet: I am a worm and no man (Psalm 21:7). His face and whole body were so disfigured by the blows and scourges that our Jesus was scarcely recognizable! Thus, the wounds he endured hid both his divinity and his humanity.

 It may be possible that the Church covers the images of the Cross during these days, for the same reason that she refrains from offering the Sacrifice of the Mass on Good Friday.

St. Thomas tells us that “the figure ceases on the advent of the reality. But this sacrament [i.e. the Eucharist] is a figure and a representation of our Lord's Passion. And therefore on the day on which our Lord's Passion is recalled as it was really accomplished, this sacrament is not consecrated.” (ST III, q.83, a.2, ad 2). In this time in which we mystically enter into the historical realities of Jesus’ final days, it is not fitting to have the image, sign or sacrament of the Cross presented to the faithful.