Because the historical and canoncial relationship of the Church of India (and the Church of all the East) is with the Patriarch of Antioch and all the East. The Coptic Pope is the Patriarch of Alexandria and all of Africa.
As per the constitution of the Indian Orthodox Church, if there is a Syriac Orthodox Patriarch of Antioch that the Indian Orthodox Church is in communion with, then that Patriarch has to be invited to preside over the installation ceremony of the new Catholicose.
Why? Why not a Coptic Pope?
But they are autocephalous (or at least consider themselves to be so), aren't they? So what's the difference for them between Coptic, Syrian or Armenian Patriarchs? All of them are Primates of separate autocephalous Churches.
The fact is Malankara (Indian) Church never officially declared autocephaly. The issue was autonomy. This ambivalence about autonomy and autocephaly can be seen in the constitution of the Malankara (Indian) Orthodox Church especially in article 1 and 2.http://www.houstonstthomas.org/stthomas/OtherItems/The%20Church%20Constitution.pdf
Look at article 1 and article 2
1 The Malankara Church is a division of the Orthodox Syrian Church. The Primate of the Orthodox Syrian Church is the Patriarch of Antioch.
2 The Malankara Church was founded by St. Thomas the Apostle and is included in the Orthodox Syrian Church of the East and the Primate of the Orthodox Syrian Church of the East is the Catholicos.
Article 114 clearly outlines the role of the Patriarch of Antioch in the installation of a new Catholicose.
114. If any one shall be consecrated as Catholicos he shall be elected to that office by the Association. If such election is approved by the Episcopal Synod, the Synod shall consecrate the person as Catholicos. If there be a Patriarch recognized by the Malankara Church the Patriarch shall be invited when the Catholicos shall be consecrated and if the Patriarch arrives he shall as the President of the Synod consecrate the Catholicos with the
co-operation of the Synod.
Article 118 of the constitution also outlines the role of the Patriarch of Antioch, when a complaint against the Catholicose arises:
118. If the complaint is against the Catholicos, the Patriarch, shall be invited and in the event of his arriving he shall be the President of the Synod and
if he does not arrive the Synod shall pronounce the decision.