Along with the direct answer to the question, there will be a small amount of extra information to make up for those who are not as knowledgeable on East and West history as the questioner of these terms.
Points to be made surrounding questions:
- Original Use
- Extended Use
- Use to identify a particular group
- How some Western people understand the word
- Particularly in regard to describing Roman Catholicism:
1.How Orthodox understand the word "Catholic" in general:
Many words can mean more than one thing. Likewise context plays a role. My understanding is that although the Orthodox Church recognizes "Universal" as a meaning, and uses it as such. The Orthodox also understand and use of this word in it's original meaning in the Greek, καθόλου (katholou), "on the whole". We need to abstract that the word as an original meaning "on the whole", but has also has been used as the meaning "Universal" as well.
I have found the words Catholic used in the Ante-Nicene and Post-Nicene fathers collection, which specifically refers to the Church in it's pre-schism state, and leans more toward the original meaning of Catholic as the "Whole" Church, made up of all the original Patriarchs. That is the Patriarchs of Alexandria, Antioch, Constantinople, Jerusalem and Rome. These are the five original Patriarchs and major centers of the One Holy Catholic(whole) and Apostolic Church, maintaining it's Orthodox (Greek for Ortho-True Doxy-Teaching) teachings (including Rome) until the Great Schism, for which Rome is separated from the other four Patriarchs. Every time the word Catholic is used in these ancient writings, it is not referring to a particular See (jurisdiction), whether it be Antioch or Rome, but simply the "whole" Catholic united pre-schism Church. Today it's still used in it's original meaning "on the whole" as well as "Universal" based on context.
-Orthodox automatically implies Catholic (but not what Protestants think when they hear the word)
Today the official title of the Eastern Orthodox Church is the "Orthodox Catholic Church",to identify themselves as the Orthodox Catholic Church. So every Orthodox Christian identifies themselves as Orthodox Catholic and a member of the One Holy Catholic and Apostolic Church. It should be noted that at every Eastern Orthodox liturgy the Nicene Creed is proclaimed in it's original form and the Eastern Orthodox Catholic Church understands themselves to be the One Holy Catholic and Apostolic Church.
This may be a week analogy, but from a complete outsiders perspective you could look at Catholic /west and Orthodox /east as something similar to Jew vs Orthodox Jew. Rome calling themselves Catholic and Orthodox being Orthodox Catholic.
It should also be noted that from an American Protestant perspective, especially those who do not know about the Orthodox Church, that the word "Catholic" has a more singular different meaning. The word brings thoughts and ideas of only Rome, teachings within Roman Catholicism, the Pope, issues before and after the Reformation, Purgatory,etc. Likewise, to say you are Orthodox to an unaware Protestant, sometimes you will be asked if you are a Jew, or in rare cases Greek Orthodox. Obviously individuals trying to related to the word, the best they can.
Going back to the Orthodox perspective, the third use of the word Catholic, is to identify the particular See of Rome. Mainly because to use the word Orthodox implies Orthodox Catholic. So yes, you will hear Orthodox very often refer to Catholic as just the See of Rome or those individuals who identify as Roman Catholic.
There are exceptions and also exceptions depending on context.. Some Orthodox choose to say the "Roman Church", not Roman Catholic, or sometimes "Romans" believing they do not have a Catholic status being in Schism, in the context of "whole". This is abstract from a sentence where someone is referring to a Roman believers Catholic heritage, for which we will address in your next question about Roman Catholicism as a word.
As you can see from the examples above, context, as well as the person you are talking to, and their knowledge, or lack of knowledge on the subject means a lot. Certain similar situations could be applied to the word Orthodox. A Syrian Orthodox could be asked if they are Greek Orthodox by a stranger they know does not understand the history, and it's easier to just say "yes", than try to describe 2,000 years of history, Orthodox Catholicism, or the relationships between the united Patriarchs of the East.
Particularly in regard to describing Roman Catholicism:
My understanding of the Eastern perspective in using "Catholicism" in "Roman Catholicism" is the following. The word is not being used in it's original Greek meaning of "whole", but rather it is being used to represent Rome's Catholic heritage and some of the theology, sacraments etc, that they still do recognize, teach, believe,etc. In this context it is as well understood as an "ism", and treated within an understanding of an individual group's teachings. "Rome's version of Catholicism".
An Eastern Orthodox Catholic Catechumen is taught that any changes that occurred within Rome's teachings, after / post Great Schism are not considered Ecumenical, not "whole", not Catholic teachings.
Out of the five pre-schism patriarchs or nine post-schism, Today Rome is still alone in many of their added post-schism teachings, while the other four original and now nine Eastern Patriarchs still hold to all pre-schism Sacraments, Holy Tradition,teachings, etc.
"Roman Catholicism" is a mixed bag of some original Catholic Apostolic teachings, sacraments, theology that were apart of their "whole" Catholic historical lineage, heritage, understanding. As well there are newly added doctrines and teachings not recognized by the Orthodox Catholic East.
Your first perspective:
Your question is very logical and your leaning toward a logical answer of Rome not being Catholic could be defended, but "only" from that single context of the word's original meaning "whole", and Rome being alone, by themselves, not "whole", with the other, now nine Patriarchs.
However going back to the context of Catholic representing historical heritage of theology, doctrine, tradition, lineage, etc. Rome is for sure "Catholic" in this context. It's true there are certain Sacraments they do not recognize, there are numerous newly added changes to many areas of Roman Catholicism that are not recognized by the Orthodox, but they are still considered Catholic from this context.
A word with multiple meanings and context means everything.