The Greek part of the Church has a different mindset to the Latin half. At the risk of over-generalisation, the Latin Romans tend to be more juridical, seeking to define as much in logical terms as possible. Also, subsequent fall of the Empire and the coalescing of authority in the Bishop of Rome as the only remaining leader in a fragmenting civilisation, gave rise to a risk of different strands of Arianism & other heresies brought on by invaders to permeate into the Church. As a result, Latin Catholics in those days refined their definitions to exclude as much misunderstanding as possible. This probably explains the centralising tendency of the Catholic Church when faced with any alternative theology.
The Greek mindset preferred to allow the Spirit to imbue us with the understanding and thus finding words unnecessary or even a hindrance to the purpose. In some ways, you may say that the contrast is similar to what we in Asia find between the pragmatic Chinese and the philosophical Indian, with all the attendant goods and bads of each position. You will notice the majority of Christological debates in the early Church and subsequent defections of Nestorians and Monophysites over them took place in the Greek half. Just an observation, not making any value judgement on anything that happened in that distant past.
Therefore, the Orthodox objects not to the doctrine but the necessity to define the doctrine. They see such things are best left to the Spirit to guide us.
Also, the Orthodox believes in a form of conciliarism, where the ecumenical council is the highest decision-making body in the church, not the Pope acting alone. As such, such a doctrine could only be promulgated by an ecumenical council of the church as a whole, including the Orthodox bishops of course. At the very least, maybe a promulgation by the Pentarchy of the five patriarchs. Definitely not by the Pope by himself, as was done in 1950. In their eyes, another example of the unilateral actions of the very monarchical First among Equals.