Because it is contained in Scripture, "Behold, I lay in Zion a chief cornerstone, chosen, and precious: He who believes in him will not be disappointed."
Elect, precious ... See the comments on these expressions under  1 Peter 2:4.  In this section of Isaiah, especially the 29th chapter which came in close connection with Peter's quotation here, the destruction of Jerusalem is foretold and also the reprobacy of the Jewish leaders who changed the word of God by their traditions; therefore, "Peter's quotation here is as much intended to show his Hebrew readers the sweeping away of the carnal Israel as to encourage them in their Christian allegiance."[23] These passages cited by Peter, especially in their Old Testament context, show that "Even while the Mosaic service was in force, the Lord was planning on another one and made predictions concerning it."[24] Scholars like to point out that Peter's quotation of these passages is "from neither the Hebrew nor the Septuagint (LXX) versions of the Old Testament, some supposing it to have been quoted from memory."[25] However, in our studies of the Pauline letters, it became clear that the inspired writers often combined Old Testament passages with their familiar phraseology to express new truth not always evident in the "quotations" cited in the Old Testament; but it should never be forgotten that the apostles of Jesus were as fully inspired (and more) than any of the Old Testament writers, and that their words, therefore, are true Scripture in the highest sense of that word, and that it is a sin to charge the New Testament writers either with "faulty" quotations from the Old Testament, or a "fallible" memory.