Sorry to interject but I'm interested in the subject matter.
"There's a difference between a caliphate and the Ottoman Empire."
There is. Broadly, Ottoman Empire originated in Turkey and Caliphate is Arab in origin. Islam was conceived in Arabia and later spread, mainly by force, to Asia Minor which includes Turkey as we now know it. Historically, this distinction alone is significant.
The Caliphate
http://www.wsu.edu/~dee/ISLAM/CALIPH.HTM
The Ottomans
http://www.infoplease.com/ce6/history/A0860176.html
http://www.cqpress.com/context/articles/epr_saudi.html
"I noticed you changed the name of the PERSIAN GULF to the Arabian Peninsula" ...."the fact that Iranians are proud of their Persian identity."
It is true that the Iranians are proud of not only their 'Persian' identity (one ethnic group approx. 51% of current population in Iran), but also of their 'Iranian' identity (many ethnic groups in Iran including Iranian-Arabs, who fought on Iran side not the Arab/Saddam side during Iraq-Iran War in the 80's).
Secondly, Ahmadinejad would naturally quip about the use of the term "Arabian Gulf", wouldn't he? Ahmadinejad may be viewed as a lunatic, but he knows how to play the popularity game at home in Iran where most Iranian people, despite the insidious efforts of IRI to Arabize Iran and even the Parsi/Farsi language, are, predominantly, still more nationalists than Islamofacists. Even & especially now, alot of Iranians realize that they were first born an Iranian not a Moslem. Thanks to IRI and their savageries in Iran over the last couple of decades for indirectly reinforcing Iranian nationalism rather than Islamisms within Iran.
Thirdly, Ahmadinejad's emphasis on "Persian Gulf" is not about being a proud persian. It is about being a Proud Shiite Moslem vs someone from Qatar, as you quote, who, most likely, is a Sunni Moslem. Syrians, and Hezbollah are Shiites too and Shiites are in the minority in the Islamic world. Furthermore, there is and has been no love lost between the Arab Sunnis and the Shiites which includes IRI.
Lastly, nationalism e.g. "calling oneself a Persian" is not acceptable by IRI wisdom. Khomeini, Khatami, and so on have repeatedly tried to brainwash Iranians and the world by saying that: nationalism has no place in Islam of their creation. Nationalism is a Western plot to undermine Islam.
I've an inkling that the situation is more complex but the above is just a flavor of what is happening.